Why are bunnies and eggs part of Easter?

Bunnies are special on Easter because they symbolize new life, which is what Spring is about. It has been a tradition to have an Easter Bunny and that is also why bunnies are so important - they keep up the tradition. Also, according to folklore, rabbits layed the eggs that the kids picked up, so without the Easter bunny, there would not be any story behind where the eggs come from.

More generally, actually bunnies are special because the whole Easter bunny tradition is focused around them.