Means "alive" in Arabic. This was the name of Muhammad's third wife, the daughter of Abu Bakr. Some time after Muhammad's death she went to war against Ali, the fourth caliph, but was defeated. This name is used more by Sunni Muslims and less by Shias.
This name began to be used in America in the 1970s, possibly inspired by Princess Aisha of Jordan (1968-), the daughter of King Hussein and his British-born wife. It received a boost in popularity after Stevie Wonder used it for his first daughter in 1975.