Anima is a person's source of power. It is the power that links the body and soul, Anima is contained in the Heart which may be one of the reasons Archdevils are so powerful due to them having two hearts they have twice the Anima. Although to use Anima properly you must bring it outside your body.
The ability to use the Anima that lays inside your body is called 'Manifestation'. As said by Heros if someone is able to master their Anima then it is possible to overwhelm their enemies with just their Manifestation.