In bluegrass music there is typically no drummer, so to keep the group together and in time, the bass player plays on beats 1 and 3, and the mandolin player plays a chop on the back-beat or the off beat, 2 and 4.
Basically, the bass player takes the place of the kick drum and the mandolin chop takes the place of the snare drum. The Banjo then plays the melody using 8th notes.