Hegira, or Hijra, is a term referring to the flight of Muhammad from Mecca, in June, 622 A.D. After its flight he became ruler of Yathrib, later called Medina, and there laid the foundation of Islam. The Moslem calendar begins with that year.
Technically, the first Hegira occurred in 615 A.D. when a group of Muslims was counseled by Muhammad to escape persecution in Mecca and travel to the Kingdom of Axum, which was ruled by a Christian king. Muhammad himself did not join this emigration.