A Nest Egg is a person's savings, which they try to keep adding to. Chickens used to live naturally and lay their eggs in nests and to encourage hens to be more productive it was common for farmers to place a porcelain egg, known as a "nest egg," into the breeding ground. It supposedly worked. And so, a small sum of money given to a person as a "nest egg" is thought to encourage them to add to it.