As the holy Quran was revealed to Prophet Mohammad during this month, the month of Ramadan is supposed to be a holy month for Muslims.
It is also believed that the doors of heaven are open and that of hell closed during this month.
Thus, this complete one month is devoted to thank god for all that he has gifted to human beings and Muslims detach themselves from all sorts of pleasures including eating and devote this month to offer prayers to Allah.
Ramadan is the ninth month of the Islamic calendar and the month of Shawwal starts after this.
It is a month of Soul purification. It is only after seeing the crescent moon that Muslims break their fast and celebrate Eid.
Eid is seen as the time to forgive all animosities and celebrate with friends and family, exchange gifts, visit places, serve delicacies etc.