Traditionally, tweet was an onomatopoeic word used to convey the sound made a small bird. It was often deployed reduplicatively, as in "The little birdie says 'tweet tweet tweet.'" This word was the origin of the name of the Tweety Bird character in old Warner Bros. cartoons.
In more recent times, a "tweet" is the somewhat unfortunate term widely used to denote a posting on the Twitter social messaging web platform. This term has also resulted in the creation of the verb "to tweet."