Muslims commemorate the fortieth day after the martyrdom of Imam Hussain (AS) and his companions, called Arbaeen, meaning the fortieth day in Arabic. They all gather around the city of Karbala and Imam Hussain’s (AS) shrine, mourning and lamenting the unfair and cruel war between his comrades and those of Yazid Ibn Muawiyah, which led into the death of those pure men and the bondage of their families. 

This commemoration happens every year around the city of Karbala. Muslims begin to walk to Karbala from other towns. They gather together in groups to pray, and especially to mourn the martyrdom of Imam Hussain (AS).
This walk is a hard one. It takes at least three days and lots of energy and time. So, why do Muslims take that? What is the philosophy behind it? 

To answer our questions, first, let’s have a review of the history behind this walk and then move to the other aspects of this commemoration. 

1. What is the Arbaeen Walk?

The history of Arbaeen walk goes back to the first visitors of Imam Hussain (AS) after his death. On the day of Arbaeen, forty days after the tragic martyrdom of Imam Hussain (AS), Imam’s (AS) son, sister and the remaining members of his family and that of the other martyrs came back to Karbala to lament the death of their dear ones besides their graves.  

Their next visitor was Jabir Ibn Abdullah Ansari on the year 61 AH. Visiting Imam Hussain’s (AS) shrine was a tradition in Shiite culture until a short period after Morteza Anasari’s became the religious reference (Marja’) of Shiite Muslims. It was then lessened for some years and then revived. Some other religious references (Marja’) kept this tradition alive among their followers, until the government of Saddam Hussain, which banned all religious Shiite traditions to be performed publically [1]. 

The tradition was revived after the fall of Saddam, and it is still to be continued. 

2. Why on Foot?

Visiting the holy shrines and going on pilgrimages on foot is not something new or belonging to our age. It’s got a long history, and Adam did the first pilgrimage on his visit to Mecca [2]. It isn’t a tradition just among Muslims either. It is performed in other faiths and religions, too. For instance, Caesar made a vow to his God to go on a pilgrimage to the Dome of Rocks if he won the battle against the Empire of Persepolis (Iran). He performed his vow after his victory [3].

Pilgrimages are highly admired, and their act is seen as a way of getting closer to Allah by Imam Sadiq (AS). Visiting the holy shrines of the twelve Imams (AS) is even more praised, especially the sacred shrine of Imam Hussain (AS). Of course, it’s not these shrines themselves that are of value and importance, but the people who have been buried there. Thus, when one makes a pilgrimage toward these shrines, he/she finds the chance to think more about these great personalities who won Allah’s satisfaction and praise and were Muslims in the real sense of the word. So, in every step that a pilgrimage takes toward Imams' (AS) shrines, especially that of Imam Hussain (AS), he/she is getting closer to a source of spiritual blessing, bringing him/her thousands of virtues and wiping away thousands of vices from his/her mind and soul.

3. What is the Philosophy behind the Arbaeen Walk?

The Arbaeen pilgrimage is not merely a long walk. Instead, it is a kind of movement in which despite being in publics, pilgrims have their own private relationship with Allah and Imam Hussain (AS), which finds a new form of divine immaterial dependence and conformance. Thinking about the goals and the history behind the martyrdom of Imam Hussain (AS), the injustice and cruelty imposed on his family and the devotions of his faithful followers brings about many personal and social growth and improvements. 

Meeting other Muslims, exchanging ideas, and making friendships with Muslims of the other countries is another social outcome of this pilgrimage. One finds out that they are not alone in their faith, and have friends all over the world. They may have differences, but they have one thing in common: Belief in Imam Hussain (AS) and his right cause. 

The last and the most crucial point to mention this great gathering is it's a kind of preparation for the grand reappearance of Imam Mahdi (AS), the awaited savior among Muslims. The Arbaeen pilgrimage is to make the minds and souls ready for this great event. It is said that when Imam Mahdi (AS) reappears, he introduces himself as the son of Hussain (AS) [6], whose fame has reached many people through the Arbaeen Pilgrimage; one of the most significant religious gathering around the world, with the estimated number of 40,000,000 people participating in it, whose news is broadcasted all over the world [5].  

References

1. "The background of Arba'een rally/The importance of Najaf-Karbala rally from the scholar's viewpoint." Fars News. Archived from the original on 16 November 2015. Retrieved 4 October 2015.
2. Hor Ameli, Muhammad Bin Hussain Vasayel-o-Shia, Vol 11, p 132
3. Sobhani, Jafar The Light of Eternity p. 696
4. Kamel-o-Ziyarat: Pp 183, 184 and 185
5. Philipson, Alice (19 January 2015). "The ten largest gatherings in human history." The Telegraph. Archived from the original on 6 October 2015. Retrieved 3 October 2015. 
6. Khademi Shirazi, Mohammad Yad’e Mahdi P16, P132

The responsibilities of a Muslim towards family, relatives and other Muslims in general, were already reviewed in an article. Here one's responsibility in Islam towards neighbors, friends, and enemies are discussed.

The Responsibility in Islam Towards Neighbors 

Doing good to neighbors is highly emphasized in Islamic teachings: “Worship Allah and … be good to … the near neighbor and the distant neighbor” (4:36). Prophet Muhammad (PBUH&HP) advised Imam Ali (AS) to honor the neighbors, even if they are disbelievers (Kafir) [1]. Imam Ali (AS) said that Prophet Muhammad (PBUH) used to invite repeatedly to doing good to neighbors such that we thought he (PBUH) was going to consider an inheritance for them [2].

The rights of neighbors on one another as an important responsibility in Islam, are:

To honor them in their presence, and to help and care about them when they are absent [3]. It includes visiting neighbors when they are sick, to assist their funeral, and to offer them your tasty meals that smell good [4];
To keep their secrets. It means that not to look for their faults and errors. And, if ever you become aware of some of their faults, do not reveal them but try to conceal their deficiencies [3];
Do not leave neighbors alone in difficulties [3]; e.g., help them in case of financial needs [4];
Do not be jealous of them if God grants them some blessings [3];
Ignore their errors to yourself and forget about them. If ever they do wrong to you unintentionally, be patient and in peace with them [3];
Do not let others talk behind their back and reveal the deficiencies of your neighbors here and there [3].
Giving priority to the neighbors. It is narrated from Imam Hassan (AS) that Lady Fatima al-Zahra (AS) used to pray firstly for the neighbors and then for members of the family [5]. 

According to Imam Sadiq (AS), having good behavior and interaction with neighbors increases the provision (Rizq) [6]. Prophet Muhammad (PBUH) advised to respect neighbors as much as one should respect his\her mother [6] and he (PBUH) said: “God bless whoever does good to his\her neighbors” [7]. On the contrary, whoever sleeps peacefully at night while one of the his\her neighbors is hungry, God will deprive him of his blessings on the judgment day [8]. The same will happen to whoever annoys his\her neighbors [1]. 

Take your time and think about these attitudes towards the neighbors. Life will be surely much agreeable and peaceful if we improve our social interactions with our neighbors within the Islamic framework.

The Rights of Friends and Companions

Having a good companion is known as a blessing; on the contrary, a bad one is like a disaster [9]. Friends and companions have certain rights one over the other including:

To interact with them with generosity as much as you can, otherwise, be fair to them [3];
To be smiling when you meet them and to receive them modestly [3];
To respect them as they respect you [3];
To be the first one who does good to the other one, otherwise, try to compensate properly [3];
To help them in difficulties and whenever they are in need, as Imam Ali (AS) advised to [10];
To hold them in great affection according to Imam Ali (AS) [11];
Not to reveal their deficiencies and mistakes;
To encourage them in obedience to God and to prevent them from committing sins [3];
To be honest with them and not to cheat [3]; e.g., nor to talk behind their back neither to reveal their deficiencies and to guard their secrets;
To be trustworthy whenever they rely on you [3].

The Responsibility in Islam Towards the Enemies

The enemy here means a person whom one is in conflict with. There are some recommendations in Islamic resources on how to treat enemies and what is one's responsibility in Islam towards them:

To be fair with them [12]. According to Imam Sadiq (AS), a real believer (Mu'min) does not oppress his\her enemies [13];
To testify in favor of the enemies if they are right [14] even if your testimony is against yourself [3];
To keep the promises you made to your enemies [15];
To forgive and tolerate them, if possible [3]. According to Imam Ali (AS), there is a virtue in forgiving enemies [16];
To talk nicely and shortly with whoever you have complained of [3], to argue with them in a way that is best (16:125), and not to ignore their rights if ever you are wrong [3].

References:

1. M. Shoueiri “Jami’ al-Akhbar”, p. 84.
2. Shaykh al-Kulayni, “Al-Kafi”, vol. 7, p. 51.
3. Imam Zayn al-'Abidin (AS), “Treatise On Rights (Risalat al-Huquq)”.
4. responsibility towards others
5. Shaykh al-Saduq, "Ilal Al-Shara'i", p. 181
6. Shaykh al-Kulayni, “Al-Kafi”, vol. 2, p. 666.
7. Shaykh al-Saduq, “Al-Amali”, p. 288.
8. Shaykh al-Kulayni, “Al-Kafi”, vol. 2, p. 668.
9. “Ghurar al-Hikam wa Durar al-Kalim”, T. 4719-4720.
10. “Nahj al Balaqa”, p. 494.
11. “Ghurar al-Hikam wa Durar al-Kalim”, T. 9665.
12. Ibn Shu’bah, “Tuhaf al-Uqul”, p. 88.
13. Shaykh al-Kulayni, “Al-Kafi”, vol. 1, p. 47.
14. Shaykh al-Saduq, “Sifat al-Shia”, p. 24.
15. “Nahj al Balaqa”, p. 53.
16. “Ghurar al-Hikam wa Durar al-Kalim”, p. 435.