The term nest egg usually refers to savings that compounds or grows with interest or through investments.
The expression is an old one and comes from a trick poultry farmer’s use to increase a hen’s egg-laying ability.
By placing a false egg, often a doorknob, in her nest, the farmer fools the chicken into laying more eggs than she otherwise would, meaning more money for the farmer, which he credits to his “nest egg.”
We call money saved for a rainy day a “nest egg”.