In music, flat means that a given tone should be one semitone lower than usual. Thus, D-flat is one semitone below D. On a piano the flat is one key lower than the base note. A B-flat is the black key below B.
In many cases, a flat note will be the same tone as the sharp note of the note below. For example, D-flat is the same tone as C-sharp. This equivalence is referred to as enharmonic. It is important to distinguish between them, however, since they will have different positions in the harmonic structure of the music.
In some rare cases, one will see a double flat. This means that the tone must be lowered by two semitones, or one full tone.
In musical notation, flat is indicated by the symbol '♭', and double flat by '♭♭'.