Staking is a process of dimpling the surrounding metal to prevent parts from coming loose. You can use a fancy tool or something as simple as a hammer and punch.
Take a look at the two screws holding the bolt carrier key on. They are staked in two places apiece. Presuming you have a Colt, of course.
A "staked" stock means you are looking at a rifle that was factory assembled with the collapsable stock as most people don't stake the nut when they install a stock. Paint is used for the purpose of telling if the parts have been separated, but don't really prevent the removal.