Christopher Columbus named the islands on his first voyage, October 1492. He called them "Las Islas de Bajamar" — "The Islands of the Low Sea" or "Shallow Sea Islands" — referring to the extensive shallow banks and reefs surrounding the archipelago (the Bahama Banks).
The name stuck because the shallows are the archipelago's defining maritime feature—treacherous for Spanish galleons, perfect for pirates, and today, a bonefish/flats fishing mecca.