At its most basic, curing of a paint is when it turns from a pliable state to a solid state throughout, not just "dry" on the surface. Curing of paint is not the same as drying as it's a change at chemical level, not merely the evaporation of liquid or binder from the paint. Practically, it matters very little to a painter, beyond oil painters knowing to wait at least six months for paint to "dry" before varnishing.
An acrylic paint feels touch dry very soon, but it takes from a few days to a few weeks to cure, depending on its thickness. To test it (at a very basic level), try rubbing a cloth dipped in turps or alcohol onto some newly dried acrylic and some that's been dried for some months, then compare how much color came off.