To 'bite the dust means' to fall, generally dead and generally in a battle of some sort. The idea is that the soldier falls down with his face to the earth. It has been used in variations such as 'bite the ground' and 'bite the earth' as well as 'bite the dust' since the 1600s.
More recently, it was commonly applied in American Western films, where Native Americans were constantly 'biting the dust'; as they attacked wagon-trains of 'brave' white settlers.