Savings, set aside for later use.
The allusion is to putting a real or china egg into a hen's nest to encourage her to lay. The connection between this and the 'savings' meaning isn't exactly clear. It may be that the idea was that the egg that was put into the nest could be later retrieved, after the hen had laid.
The practise of putting eggs into nests as an inducement to laying more is recorded from as early as the 14th century. The use of nest-egg' to refer to savings goes back to at least 1686. In 1927, Locke & Clarke printed a set of letters from that date, which included this:
"The rest, I perceive, he is not troubled should remain as a nest egg till a farther occasion."