Primarily used to mean that persistence will achieve a difficult or unlikely objective (in the US, continual is often used for constant).
The saying is recorded from the mid 13th century, but a similar thought is found in classical Greek, in the Fragments of Choeriuls of Samos, 'with persistence a drop of water hollows out the stone', and in Latin, in the Elegies of Tibullus, 'length of time eats away stones with soft water. '