Why would a chicken bite the butt of another chicken?

Answer 1

It could be that the chicken being pecked has bugs and the other chicken is being friendly and killing the bug. I have seen this happen with my own chickens and found, on closer inspection, the chicken that was pecked had a few Northern fowl mites

Answer 2

Some chickens are aggressive but most will not bother you in the farmyard. Chickens sitting on a nest are protective of their space/eggs and will peck at any hand searching for those eggs. Broody hens are at their most aggressive nature simply because they do not wish to be bothered. Roosters will "attack" strangers because their job is to protect the flock but they usually kick and flap their wings rather than actually peck at you.