The Hijra, or withdrawal, is the emigration of Muhammad and his followers to the city of Medina in 622 AD. Alternate spellings of this Arabic word in the Latin alphabet are Hijrah, or Hegira in Latin.
Muhammad, preaching the doctrines of one God (called Allah) and the threat of the Day of Judgment, did not at first have much success in the city of Mecca. His tribe, the Quraysh, which was in charge of the Kaaba (a shrine to Arabic pagan gods), persecuted and harassed him continuously.
He and his followers emigrated to the city of Yathrib, later called Medina, on July 16, 622 AD. This event marks the beginning of the Islamic calendar (1 AH, anno hegirae, or "in the year of the hijra").
There is also an unrelated social group in India called "hijra", see hijra (India).