It's the name of the moon goddess Eostre. The story that I heard was that she instructed her servant the hare to tell the people not to be afraid when the moon disappeared because the goddess hadn't gone away she was just doing private stuff. The hare, who sounds like a template for Bugs Bunny, did the opposite, told everyone it was the end of the World, doom, doom etc.
When the goddess returned to quell the riots she appeared as a beautiful bird that laid an egg for the children, and she punished the hare by cutting off his long beautiful tail.
Hence eggs and bunnies.