A symbol, placed before a notehead on staff-notation, or placed after a nominal in text, which indicates a change in pitch of one chromatic semitone lower than that of the plain nominal. The flat is a specific type of accidental.
A note with a flat is also one diatonic semitone higher than the plain nominal just below it, i.e., A:Bb is a diatonic semitone.
The flat sign evolved out of the "round-b" notation which was used to indicate the lower version of the note "B" which appears in the synemmenon tetrachord of the lesser perfect system.
In a general sense, "flat" simply means lower in