Drying is the process of getting the moisture level in your buds to the point where they are not in danger of molding.
Curing is bringing the moisture level to a point where it is even throughout the bud itself. A newly-jarred bud will be moist on the inside and dry on the outside. After a proper cure, it will be even throughout.
The jar is to prevent further moisture loss as the bud cures.
Another important aspect of the cure is that it allows any remaining chlorophyll to degrade. This diminishes the harshness of the smoke, and allows for the pure clean flavors of the bud to come through.