Fasting the Month of Ramadan:

Every year in the month of Ramadan,⁴ all Muslims fast from dawn until sundown, abstaining from food, drink, and sexual relations.

Although the fast is beneficial to health, it is regarded principally as a method of spiritual self-purification.  By cutting oneself off from worldly comforts, even for a short time, a fasting person gains true sympathy with those who go hungry, as well as growth in his or her spiritual life.

The Pilgrimage to Makkah:

The annual pilgrimage (Hajj) to Makkah is an obligation once in a lifetime for those who are physically and financially able to perform it.  About two million people go to Makkah each year from every corner of the globe.  Although Makkah is always filled with visitors, the annual Hajj is performed in the twelfth month of the Islamic calendar.  Male pilgrims wear special simple clothes which strip away distinctions of class and culture so that all stand equal before God.

Pilgrims praying at the Haram mosque in Makkah.  In this mosque is the Kaaba (the black building in the picture) which Muslims turn toward when praying.  The Kaaba is the place of worship which God commanded the Prophets Abraham and his son, Ishmael, to build.

The rites of the Hajj include circling the Kaaba seven times and going seven times between the hillocks of Safa and Marwa, as Hagar did during her search for water.  Then the pilgrims stand together in Arafa⁵ and ask God for what they wish and for His forgiveness, in what is often thought of as a preview of the Day of Judgment.

The end of the Hajj is marked by a festival, Eid Al-Adha, which is celebrated with prayers.  This, and Eid al-Fitr, a feast-day commemorating the end of Ramadan, are the two annual festivals of the Muslim calendar.

Footnotes:

(4) The month of Ramadan is the ninth month of the Islamic calendar (which is lunar, not solar). 

(5) An area about 15 miles from Makkah. 

Source: A Brief Illustrated Guide to Islam