The Cambridge dictionary defines wisdom as using knowledge and experience to make good decisions and judgments. (1) The most similar equivalent for this word in Arabic is the word  “حکمة” (“Hikmah”) which denotes justice, knowledge and tolerance. (2) 

This word has been used so many times in the holy Quran and has a special meaning in  Islamic literature. The holy Quran says:
Allah grants wisdom to whomever He wishes, and he, who is given wisdom, is certainly given an abundant good, and none takes admonition except those who possess intellect. (2:269) 
About this verse of the Quran, Imam Sadiq (AS) says:
(In this verse) Allah The Almighty has portrayed the intellectuals in the best way. (3)

Hikmah is the message of the Prophets

Allah The Almighty has rapidly pointed out this fact that He has sent the prophets with “Hikmah” and they should teach people how to be wise. The holy Quran says:

Allah certainly favored the faithful when He raised up among them an apostle from among themselves to recite to them His signs (the verses of Quran) and to purify them and teach them the Book and wisdom, and earlier they had indeed been in manifest error. (3:164)
And:
There have already come to them, reports (via the Prophets) containing admonishment, [and representing] far-reaching wisdom; but warnings are of no avail! (4:54)
Also: 
Invite to the way of your Lord with wisdom and good advice and dispute with them in a manner which is the best manner.. (16:125)
And: 
When Jesus brought those manifest proofs, he said, ‘I have certainly brought you wisdom, and [I have come] to make clear to you some of the things that you differ about, so be wary of Allah and obey me. (43:63)

Allah almighty even says that the holy Quran is a book full of wisdom:
These are among [precepts] that your Lord has revealed to you of wisdom. (17:39)
These are the signs of the wise Book (31:2)

What is wisdom in the eyes of Allah?

The original meaning of the word “Hikmah” is wisdom, knowledge and tolerance and the ability to use your knowledge in the best way; but Allah The Almighty prefers some special kinds of wisdom. The verses of the Quran and the hadiths, try to clarify the true meaning of wisdom from Islamic sight.

Obedience towards Allah 

•    Abu-Basir, one of the brilliant pupils of Imam Sadiq (AS) once asked him about the verse; “He grants wisdom to whomever He wishes (2:269)”. Imam Sadiq (AS) replied, “That (Wisdom) is obeying Allah and knowledge about Islam” (4)
•    Imam Baqir (AS) also says that “Hikmah” means: “not to commit the sins that Allah has ordained for it the Hell as a punishment” (5)
•    Once Prophet Muhammad (PBUH & HP) asked a group of people who they are.
They said that they are some faithful people.
The Prophet (PBUH & HP) asked: “What are the signs of your faith?”
They said: “We are content about what Allah has planned for us and we are submissive to the order of our God and we trust in him for everything.”
The Prophet said: “You are so knowledgeable and wise the way that your wisdom can almost make you like prophets.” (6)

Knowing our Imams

Imam Sadiq (AS) about the verse “…and he, who is given wisdom, is certainly given an abundant good (2:269)” said ,“The abundant good is knowing Imam Ali (AS) and the other Imams (AS)” (7) 
He also said: “(The “Hikmah” mentioned in the verse is) obeying Allah and knowing the Imam (of your time)”
In Arabic, the word “جهل” (Jahl) means “Ignorance”, which can be considered the opposite of “Hikmah”. So anyone who is not “Hakim” (wise) is “Ignorant” in Islamic culture. There is a hadith narrated from the Prophet (PBUH & HP) in which he said:

Anyone who dies while they don’t have an Imam will have died like a person in the ages of ignorance (8)

This hadith has been narrated by all Muslims’ Sunnis and Shiites and the authenticity of this record is undeniable. 
About knowing the Imam, Imam Sadiq (AS) also said:
Anyone from among the followers of Prophet Muhammad (PBUH & HP) who understands the status and the rights of their Imam, will find how delightful  having faith is.(9)

Understanding Religion

The last meaning of “Hikmah” mentioned in the Hadiths is “Fiqh” (jurisprudence) which means “Understanding”. In Islamic culture, this word is  employed  to define a deep understanding of religion and profound knowledge about  it . (10)
Imam Sadiq (AS) said: 

“Hikmah is the knowledge about religion and understanding it (Fiqh). Therefore, anyone who understands the teachings of the religion is a “Hakim” (a wise person). Indeed above all, Satan wishes the ones who deeply understand religion, to be dead.” (11)
The Holy Prophet (PBUH & HP) said: 
Allah has given me the Quran and he also gave me Hikmah just like the Quran and every house which therein is no Hikmah is nothing but a ruined place. So learn Fiqh and get to know the religion so that you don’t die like ignorant people. (12)

To wrap up, in the Islamic view, “wisdom” means knowing how to live as a good servant of Allah and living the same way. As you see, all the meanings mentioned in the Quran and the Hadiths are about knowledge of religion and living the way religion indicates. Knowing your Imam (who is the leader Allah has chosen for you) is the best way to understand what you should do and how you should obey the orders of Allah.  It is then obvious that all these different meanings and teachings employ a common concept which is obeying the order of Allah after having enough knowledge about it.  
It is then obvious that all these different meanings and teachings employ a common concept; obeying the orders of Allah after gaining and enjoying competent knowledge about them.

Resources

1.  https://dictionary.cambridge.org/dictionary/english/wisdom 
2. Al-Ain, Khalil ibn Ahmad al-Farahidi, vol.3, pg.66
3. Al-Kafi, Sheikh Koleini, vol.1, pg.13
4. Tafsir noor ath-Thiqhlain, al-Huvaizi, vol.1, pg.287
5. Tafsir, Al-Ayyashi, vol.1, pg.151
6. At-Tohid, Sheikh Saduq, pg.371
7. Tafsir noor ath-Thiqhlain, al-Huvaizi, vol.1, pg.287
8.  Musnad Ahmad ibn Hanbal, vol.28, pg.88
9.  Basa’ir ad-Darajat, Muhammad ibn Hassan as-Saffar, pg.412
10.  Sihah, al-Johari, vol.6, pg.2243
11.  Tafsir, al-Ayyashi, vol.1, pg.151
12.  Majma al-Bayan, Sheikh at-Tabarsi, vol.2, pg.194
     

“Modesty and faith are connected with one another just like two things fastened by a rope. If one of them is gone, the other is also lost” [1]. Imam Baqir (AS). Modesty is a special sense that prevents one from saying inappropriate words and making mistakes. It refers to an uncomfortable feeling accompanied by embarrassment, caused by one's anxiety about being exposed to some unworthy or indecent conduct. This concept, as one of the highest and most fundamental moral qualities, is known as Haya in Islam. Modesty in Islam describes shyness and shame, but Haya represents a more profound implication that is based on faith. In many sayings (Hadiths), it has been quoted that modesty is linked with faith and originates from it [1, 2]. Hence, it is one of the most important characteristics that every Muslim should acquire and possess [3]; particularly Muslim women (“haya is a good characteristic for all, but is better for women” [4]).

Modesty in Islam: natural and acquired

There are two types of modesty: natural and acquired. An example of the former is the feeling of shyness and humility naturally occurring in a young child that makes him/her cover the private parts of the body from others. Or, in the story of Eve and Adam (PBUT) where they realize their nakedness and try to hide their genitals. This kind of modesty is common sense that exists within all human beings, believer or non-believer: “God Almighty divided the modesty among people just as He divided the provision” [5], and what differentiates them from animals: “If modesty did not exist … the promises wouldn’t be kept … Nobody would do any good, and nobody would refrain from the evil … if it weren’t for modesty, many people wouldn’t stop sinning.” [6]. Modesty serves as a cover on the soul that conceals the defects and calms down wrath and lust [7]. No one can, therefore, justify his/her sins and mistakes because of not being naturally given a sense of modesty.

The latter, on the other hand, can be only attained as a result of knowing and perceiving the Glory of Allah and minding His presence everywhere and in every second. In Islamic ethics, modesty is more than just a question of how a person dresses and acts in social interactions; instead, it is reflected in a Muslim’s conduct before God, before others, and even when one is alone.

Modesty towards others

Modesty towards others entails that one has decent and reasonable behavior in public, avoids indecent talks and vain activities, and respects everyone around him/her. If one has developed this ethical aspect within him/her and obeyed this sense, he/she will become ashamed when someone notices him doing something wrong. This feeling will be even worse when the other person is in a higher position. This, consequently, stops him/her from repeating that action.

To clarify the importance of modesty towards people, Imam Ali (AS) said that the evilest of all is who is not ashamed of his actions in front of people [8].

Modesty towards others includes especially the opposite gender and involves not gazing at them [9], harming them in any way or indulging in any forbidden (Haram) relation with them. In Surah Nur, Allah guides both men and women to the key to modesty by saying that believing men and women should lower their gaze and guard their modesty (24:30-31).

A good instance of modesty in the interactions between opposite genders is described in Surah Qasas, verses 23-26, between the daughters of Shoaib (PBUH) and Moses (PBUH). These verses demonstrate that the daughters of the prophet work and appear in society, but they care about how they interact with others; they concentrate on what they should do without having unnecessary dialogues with men. They communicate as much as necessary, with respect and dignity. Their speech is direct and clear-cut with Moses, so are Moses’s words. Even the way they both walk is with care and shyness [10].

Modesty towards Oneself

Modesty towards oneself means that a person treats himself fairly in private. It is caused by the unpleasant feeling that arises when thinking of or doing something improper which consequently stops one from forbidden (Haram) thoughts or illicit acts. It was mentioned that when one does something indecent and suddenly notices the presence of others, he becomes ashamed (if he still possesses the natural modesty that is laid within his soul); a higher level of Haya is being ashamed of oneself when no one else is present. This kind of modesty is known as the yield of faith: “The shame a person feels from himself originates from [his] faith.” [11].

Modesty towards God

Modesty towards God is called the best level of modesty [12]: “be modest in front of Allah for He has a right to your modesty” [13]. To accomplish this, one should first believe that nothing can be concealed from God “Does he not know that Allah sees [him]?” (96:14). In fact, Allah sees and knows everything, and is closer to humans more than themselves: “and We are nearer to him than [his] jugular vein” (50:16). Consequently, a modest person toward God will avoid any indecent act, in public or private, and will leave sinful thoughts behind.

References:

1. M. al-Kulaynī, “Al-Kafi”, vol. 2, p. 106.
2. M. B. Majlesi, “Bihar al-Anwar”, vol. 75, p. 309.
3. M. al-Kulaynī, “Al-Kafi”, vol. 2, p. 106, T. 5.
4. A. Q. Payande, “Nahj Al-Fasahah”, p. 578, T. 2006.
5. S. H. al-Amili, “Wasail al-Shia”, vol. 20, p. 135.
6. M. B. Majlesi, “Mofazzal monotheism”, Chapter: Human Senses.
7. “Nahj al-Balagha”, no. 223
8. “Ghurar Al-Hikam”, no. 5464
9. M. B. Majlesi, "Bihar al-Anwar”, vol. 101, p. 40.
10. N. Makarem Shirazi, “Tafsir Nemooneh”, vol. 16, p 58-59.
11. “Ghurar Al-Hikam”, no. 4944.
12. “Ghurar Al-Hikam”, no. 5451.
13. H. T. Nuri Ṭabarsi, “Mustadrak al-Wasail”, vol. 8, p. 462.