Every God in the God of War universe, hold some sort of power, that makes them gods. These powers can be anything from summoning magic, to pure physical strength. Some powers can be used by Kratos if he kills the gods/goddesses. But to do so, he needs to pick up the source of the power from their bodies. This is because Kratos himself cannot learn magic just by killing. But he can use the gods items against them.
Such items can be, but are not limited to, Zeus' Gauntlets, Hermes' Boots, Hades' Claws, Thor's Hammer or even Odin's spear. By killing the god who holds these items, Kratos will be able to pick them up and use them as his own.