Hajj:

It occurs on the eighth day of Dhul-Hijjah (Zul-Hijjah) the 12th month of the Muslim lunar calendar. It falls on a date about 11 days earlier each year. See Hajj (Start): wincalendar.com Upon arriving in Mecca, pilgrims gather in the courtyard of the Masjid al-Haram around the Kaaba . They then circumambulate—tawaf in Arabic—or walk around the Kaaba 7 times, during which they hope to kiss and touch the Black Stone (al-Hajar al-Aswad) embedded in the eastern corner of the Kaaba. Because of large crowds it is ok to just point at it now.
They are also expected to go to the the Well of Zamzam at Makkah 66 ft east of the Kaaba.
According to Islamic belief and the Bible, it is a miraculously generated source of water from God, which began thousands of years ago when Abraham's infant son Ishmael and his Mother Hagar, Ibrahim's (Abraham's) wife's servant, was thirsty and kept crying for water. Muslims reenact Hajar's (Hagar's) search for water when they pace 7 times between the hills of Safa and Marwa. Marwah is located about 1,150 ft from the Kaaba. The distance between Safa and Marwah is approximately 1,480 ft, so that seven trips amount to roughly 2 mi.

There are some differences in the Bible and Islamic stories.
In the Bible [Genesis 21:8-19] Hagar and Ishmael go away after Isaac is born, so Ishmael is a young boy and they go to Beersheba (in modern-day Israel).

According to Muslim Sunnah (sayings and teachings of Muhammad. It's not in the Qur'an), Abraham left Hagar and Ishmael in Bakkah (the ancient name for Mecca). Mecca is in the middle of a searing desert, some 750 miles from Beersheba and Ishmael is an infant.
See Hagar and the Well of Zamzam: how a woman discovered one of the holiest sites in Islam

Links:
Hajj 2014, Islam's Pilgrimage To Mecca: Facts, History And Dates Of The Muslim Holiday
Hajj - Wikipedia