In the Bible, Ishmael was Abraham's son by Hagar. He and his mother were driven out of Abraham's household after Abraham's wife Sarah gave birth to Isaac. In the Qur'an (the holy book of Muslims) Ismail (Ishmael) who is Abraham's son was the one that was nearly sacrificed - not Isaac.
In the Quran, he is known as the first-born son of Abraham from Hagar. Islamic tradition also believes that he was the one-nearly sacrificed, not Isaac (or Ishaq in the Quran). Abraham's willingness to sacrifice his son for God is celebrated in Eid ul-Adha every year by Muslims.
Islamic tradition also holds that Ishmael helped his father build the Kaaba in Makkah. Ishmael is also supposidely buried near the Kaaba on the grounds of the Masjid al Haram. Ishmael is also important due to the story of how he and his mother were in Makkah without water. The frantic running of his mother in pursuit of water, only to be followed with a miraculous spring springing from the ground is used to describe the Zamzam Well. Muhammad is considered a direct descendent of Ishmael.
Other Ishmaels:
Ishmael in Islam