Why are eggs associated with the Easter bunny?

The Easter bunny and the Easter eggs

Both eggs and rabbits have to do with fertility. Spring festivals tend to be about fertility and rebirth. This is a tradition that is older than Christianity and was coopted by Christianity when it was becoming a popular religion. As a recent religion, Christianity was usually smart enough not to mess with the local celebrations but just adapt them a little bit. That made it easier for people to go along.

From pagan religion, both the egg and the bunny are symbols of fertility. In the pagan religion, Easter was the "spring festival", celebrating fertility and requesting that the Gods give good crops. It makes sense that the rabbit and the egg would be symbols of spring festival.

Easter is also a symbol of the Anglo-Saxon goddess, Eostre, as the holiday was originally named after. Easter is a relatively new adoption of spelling which was used, as said above, to help make the coexistence and/or transition of religions go much smoother.