The word "acoustic" is derived from the Latin term for the ear canal. Acoustics is therefore the branch of science which studies sound. By derivation, "acoustic music" is that which is made naturally, without the use of electricity, electronics, etc. Think of it as any type of natural sound. It is essentially synonymous with the term "unplugged."
Acoustic includes a broad range of musical genres, the common theme being that the music is played without amps, electronic keyboards, or any instrument which needs to be plugged into an electrical circuit.
The term originally developed to denote the type of music which is played on an acoustic guitar as opposed to an electric guitar.