It is thought that the idea of the Easter Bunny was developed by German Protestants, who wanted to retain or re-introduce the Catholic custom of eating colored eggs for Easter, but did not want to introduce their children to the Catholic rite of fasting, which was the reason for the abundant availability of eggs at Easter time (they were forbidden to Catholics during the fast, thus eggs layed during the fast were stored until the feast).
The idea of an egg laying rabbit came to the United States in the 1700s. German immigrants in the Pennsylvania Dutch area told their children about the "Osterhase" (also: "Oschter Haws") or Easter Bunny. Only the good children received gifts of coloured eggs in the nests that they had made in their caps and bonnets before Easter. Presumably, the Oschter Haws laid them when they were not looking.
In the United States, the Easter Bunny purportedly leaves baskets of treats (including Easter eggs and assorted chocolates) on Easter morning for good children. This is a common practice even in non-Christian households, as Easter has started to become a more non-sectarian festival, like Halloween or Valentine's Day.