A girl who looks or behaves like a boy. Girls who are tomboys tend to be very athletic and sporty.
They almost always dress like boys and in anime frequently have short and/or spiky hair and can often be seen wearing tight cycling shorts. Examples would be Kagura (Azumanga Daioh), Arisawa Tatsuki (Bleach) and for a videogame example, Makoto (Street Fighter III: 3rd Strike).
Similar to the androgynous tag, but differs in that androgynous apply to both men and women, referring to possessing physical traits associated with both sexes (not usually in terms of genitals, but rather facial features and build). An androgynous person wouldn't necessarily be a tomboy at all (they may actually be male anyway) but a tomboy is somewhat androgynous. A girl whose androgyny results in a very masculine appearance is referred to as a reverse trap.
Note: Just having short hair is not enough to count as a tomboy. The girl in question has to dress and act in a masculine manner.