The legend of the Easter Bunny is far from a modern invention. Long ago, the rabbit was the earthly symbol of the pagan goddess Eastre, and was worshipped in the pagan festival of Eastre.
Germans brought the legend of the Easter rabbit to America, though Easter itself wasn't widely celebrated in America until after the Civil War.
The hare has long been a symbol of fertility and renewal of life -- which fit in with the Christian tradition of Easter and the tradition of Easter eggs.
In the United States, the Easter Bunny is fabled to lay the eggs in the nests prepared for it or hide them for children to find.