Convince Creature Runes are used in battle on creatures to convert them to your side.
Some Creatures can not be Summoned but they can be convinced.
Unlike Summoned Creatures, convinced creatures can drop loot (unless a summoned creature is convinced).
Also, on PvP worlds, a player's summon (excluding monks) can be caused to defect from your enemy and fight for you, or, as a paladin or a knight, you can convince creatures summoned by a mage; for instance a paladin can pay a mage to summon a demon skeleton and can convince it to help him hunt dragons.
NOTE: This strategy doesn't work anymore. As of Aug 09, 2011 convincing other players' summon is not possible anymore.