A detailed sequence of actions to perform to accomplish some task. Named after the Iranian, Islamic mathematician, astronomer, astrologer and geographer, Muhammad ibn Musa al-Khwarizmi.
Technically, an algorithm must reach a result after a finite number of steps, thus ruling out brute force search methods for certain problems, though some might claim that brute force search was also a valid (generic) algorithm. The term is also used loosely for any sequence of actions (which may or may not terminate).
Paul E. Black's Dictionary of Algorithms, Data Structures, and Problems.