to the Biblical story in which Jesus is resurrected (the reason Christians celebrate Easter), pointing to another appropriation of pre-Christian religious figures, symbols and myths by early Christianity.
The Easter Bunny is German in origin. He first appears in literature in 16th century as a deliverer of eggs. All rabbits and hares were thought to lay eggs on Easter Day, but the Easter Bunny specifically sought out and rewarded well-behaved children with colored eggs in a manner reminiscent of Yule customs. The movements of the hare, leaping and zig-zagging across the fields, were thought to hold clues to the coming year.
Eggs themselves are obvious symbols of resurrection and continuing life, as well as fertility. Early humans thought the return of the sun from winter darkness was an annual miracle, and saw the egg as a natural wonder and proof of the renewal of life. As Christianity spread the egg was adopted as a symbol of Jesus' resurrection from the tomb.
So, observant Christians who are aware of the origins and folklore surrounding bunnies and eggs celebrate Resurrection Sunday in keeping with Biblical teachings. Others celebrate Easter.