1. Stay calm, retain self-control, as in When the rowboat capsized, George yelled that everyone should keep their head and hold onto the boat . This usage dates from the early 1600s and is about two centuries older than the antonym, lose one's head, meaning "to become confused and agitated," as in Whenever the stock market goes down sharply, people seem to lose their heads and sell.

2. keep one's head above water. See head above water.