Possession is an ability a Caster, Vex, and occasionally an Incubus has. It is the ability to take the vessel of a living being and take over their body, while the host's soul is "dormant." Casters who possess Mortals are still able to use their powers, as seen with Sarafine. When they possess mortals, they still their retain their powers and abilities.
Sarafine Duchannes is known to do this with Mrs. Lincoln. She says that she hated possessing Mrs. Lincoln, so much she wanted to kill Link because he was so annoying, and talked about his band.