Why do muslims fast?

Here are some possible reasons why Muslims observe a marathon one-month fast during Ramadan.
(a) To obey Allah's injunction
Fundamental to a Muslim's faith (or belief) are six articles: (i) belief in Allah, (ii) belief in Angels, (iii) belief in divine Books of Allah, (iv) belief in all Prophets, (v) belief in the Day of Judgement, and (vi) belief in Predestination. Articles (i) and (iii) demand that a Muslim must believe in, obey and implement, all the words of Allah contained in the Holy Qur'an. This is because ...His (Allah) word is the truth..." (6:73) and ::the truth is from your Lord, so be not at all in doubt" (2:147) and "...whose word can be truer than Allah?" (Qur'an). Thematically, Qur'an contains injunctions for mankind, allegories, stories of past events, accounts of future events, and a lot of lessons especially for Muslims. Of importance the injunctions are sometime directed to all creatures (men and jinns), or sometime to specific gender (men or women), or sometime to specific tribes (eg "Bani Israel"), or sometime to the progeny of Adam (i.e mankind), or sometime to Ahl-ul kitaab (the people of the book), or sometime to Muslims (i.e those who believe in One Allah) etc. In most cases, the injunctions of Allah to Muslims can be regarded as blessing and mercy and when fully obeyed often lead them to His straight path. Without mincing words, there is no compromise with Allah's injunctions: every sincere and God-fearing Muslim must obey them; this is a necessary precondition for being a Muslim. One of His injunctions, directed to Muslims (men and women), is:
"O you who believe, fasting is prescribed for you..."(2:183)
The phrase "O you who believe" is referring to: (i) those who submit to Allah's wills and commands, (ii) those who believe in the six articles of faith, (iii) those who testify that "La ilaha illa llaha Muhammadu-r Rasululla", (iv) those who practise the five pillars of Islam, and (v) those who implement and obey Allah's injunctions in the Qur'an and follow the sunnah of His Prophet, Muhammad (s.a.w). No followers of any religions satisfy these criteria of "O you who believe" except the Muslims. It is they (Muslims) that Allah is directing His injunction in 2:183 to. The injunction prescribed fasting as a compulsory duty for them thus:
"...fasting is prescribed for you (Muslims)..." (2:183)
and
"...whoever witnesses the month of Ramadan should fast through it..." (2:185)
Clearly, Ramadan fast is a divine injunction mandatory for all able-bodied Muslims who are free from compelling excuses. Whoever deliberately forgoes fasting in Ramadan, should know that (s)he has disobeyed Allah's injunction and no amount of fasting thereafter can give her/him a reward equivalent to one misssed Ramadan fast as obvious in this hadeeth:
Abu Huraira reported that the Prophet(s.a.w) said: "whoever did not fast one day of Ramadan without a genuine excuse or a disease then even if he fasted for a complete year, it would not compensate for that (missed Ramadan) day"
(Sahih al-Bukhari, vol 3,p.88)
(ii) To practice the tradition, and way of the pious people.
Fasting is not new to Islam; it is, indeed, as old as Adam(a.s) who was the first creature and the first Muslim to submit to one Allah. No one knows precisely when fasting began among Adam's progenies but it is the practice of all the Prophets of Allah and their followers. Qur'an mentions that Musa(a.s) fasted for 40 days (see 2:51) (this is what the Jews termed "Jewish Passover") and the Prophet(s.a.w) told us that Dawud(a.s) used to fast for half of the year (this involves fasting on every alternate day). 'Issa (a.s) (or Jesus) was also reported to have fasted for 40 days (this is what the christians termed "the Lent", usually observed before Easter festival). Since these Prophets were Muslims, it can be seen that by asking Muslims to fast, Allah intends to draw their attention to the practice and tradition of those pious predecessors who attained piety (in His sight) through fasting.
"O ye who believe, fasting is prescribed for you as it was prescribed for people before you ..."(2:183)
This verse shows that fasting was observed by the people (i.e "ahl-ul kitaab") who came to the scene before the Muslims and so it is a "sunnat Allah" (i.e a tradition approved by Allah) for those who lived aforetime and for the Muslims who are now the best generation ever raised for mankind (3:110). Qur'an says:
"(As for) the sunnat Allah (approved) for those who lived aforetime, no change will you find in (such) sunnat-Allah" (33:43)
Therefore, Ramadan fast should be seen as a propagation of the tradition approved by Allah for all those who submit to Him.
(iii) To learn how to attain piety
By the very nature of human beings, they are susceptible to sins and transgression of Allah's limits. This may be due to their ignorance, worldly struggle for ephemeral and tantalizing things, or satan's handiwork. In particular, Muslims are warned against gossiping, backbiting, slandering, hypocrisying, lying, cheating, duping, hatring, nursing grudge, keeping malice, fornicating as these vices negate the teachings of the Holy Qur'an. But since Muslims are like any human beings created to err as a result of forgetfulness, they need to be reminded and coached against any social vices from time to time. This will requires a fixed trainning period where Muslims will know and learn how to put an end to vices, learn virtues and get nearer to Allah. That trainning period is chosen by Allah to be the Ramadan fast which occurs once in every year. During Ramadan:
(a) compulsory five daily salaat are observed regularly and timely (this is to remind and train the mindless Muslims that salaat is an all-time duty for them); (b) Zakat-ul fitr is paid on or before the 'idl Fitr (the festival that commemorates the end of Ramadan fast) (Zakat-ul fitr is to teach Muslims to do sadaqah and to remind them that after zakat-ul fitr they should not forget to pay on time their annual divine obligatory Zakaat, the fourth pillar of Islam); (c) Tarawih and Tahajjud prayers are observed in the evening and night of Ramadan (this is to teach Muslims to observe nawafil (i.e additional) prayers after Ramadan so as to increasetheir iman and get their supplications to Allah accepted promptly);(d) Doubtful hobby such as smoking is stopped (this is to train Muslims to be frugal as Allah hates extravagancy and to save themselves from diseases such as Tuberclosis, Cancer, and heart attack known to be associated with smoking and premature death);(e) pornographic videos/pictures are avoided and kept away (this is to free Muslims' hearts and eyes from corruption and from shaitan's whisperings to do evil deeds); (f) Excessive intake of food is avoided (this regulates the stomach from being pot-bellied and distinguishes Muslims from kaafir whom Qur'an describes as those who eat like cattle (47:12)); etc. All these good things which Ramadan fast teaches Muslims are the means to attain piety. This is why the verse on Ramadan fast says:
"O ye who believe, fasting is prescribed for you...so that you will (learn how to attain) piety" (2:183)
(iv) To reap the full reward of the Night of Power (Lailat-ut Qadr)
The last book of Allah to His creatures, Al-Qur'an, was revealed in the night of Ramadan. What this means is that the first divine revelation to Prophet Muhammad(s.a.w) took place in the Night of Ramadan. Allah chose the night because of the special blessings in it. It is called the night of Power (Lailat-ut Qadr) or the night of blessing (Lailat-ul mubarak). The deed in this night is better than the rewards of deeds of 1,000 months (about 83.3 years). Let suppose that a man survived up to 100 years and he consciously witnessed 93 nights of Power, he would have in his account more than 7,750 rewards which exclude all other rewards he earned from doing virtuous deeds. It is this night that all Muslims are invited by Allah to look for in the month of Ramadan. Specifically, the night is in the last ten days of Ramadan and usually in one of the odd days (i.e. 21, 23, 25, 27 and 29th). A Muslim is expected to perform naafilah, recite the Qur'an, do zikr etc in the night. Since no one knows precisely which of the odd days is the night, Muslims are expected to be in seclusion (itikaf) during the last 10 days of Ramadan and the best place to do so is in the mosque.
It should be mentioned that the Angels descend in succession during the night of Power and they go round with special greeting of "peace" till day break when they will move back to their position. The number of these angels is uncountable and they descend with special command of Allah. The following chapter of the Qur'an details the event of the night of Power thus:
"Indeed We have revealed it (Qur'an) in the night of Power. And what will explain to you what the night of Power is? The night of Power is better than a thousand months. Therein descends the Angels and the Spirit by Allah's permission, on every errand: (they say) Peace" (continuously) till the rise of Morning!" (97:1-5)
Who will like to miss the Night after reading this description? It is this very reason that every Muslim wants to witness and reap its full blessing by fasting during the days of the month of Ramadan. As Ramadan fast is inextricably tied to the Night of Power (see 2:183) it follows that any Muslim who wishes to benefit from the Night of Power must fast during the month of Ramadan. Qur'an says:
"Ramadan is the (month) in which Qur'an was sent down, as a guide to mankind, and a clear guidance and judgement (so that mankind will distinguish right from wrong). Whoever among you witnesses the month of Ramadan should fast through it..." (2:183)
(v) To show to Muslims how to get their past sins forgiven
Islam is a religion that stresses equality: both the poor and the rich (men or women) are equal as slaves in the sight of Allah. In Islam the surest way to obtain Allah's forgiveness for one's past sins is Pilgrimage (the fifth pillar of Islam) which unfortunately is easy for the rich to afford the cost of the journey. The All-wise, Allah, did not put the poor Muslims in limbo, rather He made fasting during Ramadan as a means of placing the poor and the rich on equal footing in terms of asking for forgiveness for their past sins. If a Muslim has no means of going for hajj, there should be a way to compensate him/her. The All-wise has chosen Ramadan for all Muslims to get their past sins forgiven as evident in this hadith:
Narrated Abu Huraira(r.a): The Prophet said:"... whoever fasts during Ramadan with sincere faith and hoping for his reward from Allah will have his past sins forgiven"
(Sahih Al-Bukhari, vol.3 p.70).
Therefore, Ramadan fast unites Muslims and bring them together as equal slaves who can be forgiven of their past sins devoid of discrimination in the sight of Allah.
(vi) To show that Fasting is the epitome of the five pillars of Islam
Islam is built upon five pillars. The third pillar is siyam (i.e fasting during Ramadan). The wisdom behind its third position is because it is a fulcrom upon which the other four pillars (Tawheed, and salaat are in first and second positions while zakat and Hajj are in the fourth and fifth positions) are balanced. It is the only pillar that encompases all the four other pillars in the sense that

Source:http://www.sunnah.org/ibadaat/fasting/fast.html