A socket is a special slot on an item into which Manastones can be inserted to provide bonuses to certain stats.
You can only add the number of Manastones that matches the number of socket slots in a particular piece of equipment. Namely, you cannot add three Manastones to an item that only has two sockets. However, to make room for new Manastones, an outdated Manastone can be removed via a Manastone Remover, and the old manastone will no longer be useful.