The answer is, nothing at all! The word Easter comes from a Germanic pagan fertility Goddess called Eostre, if you speak Old English, or Ostara, if you speak Old High German. It just so happens that the month we call April, the people who spoke Old English called Eostre's Month.
The first mention in history of the original Easter festival comes from no less than the Venerable Bede, a brilliant monk who lived in England in the 600s AD. Bede was a major player in the hot subject of his day: how to calculate when the death and rebirth of Jesus should be celebrated. He wrote a book about it called De Ratione Temporum which means On Calculating Time.
Bede's calculation landed the Christian event in Eostre's Month (April!). Bede commented in the same book, in an almost offhand way, that Eostre's Month traditionally saw the locals hold festivals in honour of the pagan goddess Eostre.
Bunnies are particularly good at doing the fertility thing, and eggs have the obvious meaning. Bunnies and eggs therefore are the symbols of the German fertility goddess. This all got mixed up with the Christian event and since no one in their right minds turns down chocolate, I don't think they'll be separating any time soon.
I went looking for a decent translation of Bede's original comment and the best I could find was from tertullian.org, who in turn got it from a translation by Faith Wallis, Liverpool University Press 1988, pp.53-54.
Eosturmonath has a name which is now translated "Paschal month", and which was once called after a goddess of theirs named Eostre, in whose honour feasts were celebrated in that month. Now they designate that Paschal season by her name, calling the joys of the new rite by the time-honoured name of the old observance.
Happy Eostre / Ostara / Easter !