God's Spirit imparts wisdom and understanding. It teaches His way of life, comforts, and helps us. Even when we cannot express ourselves in our prayers, the Spirit aids us in making our requests before God.
The meaning is so clear: The Father and the Son live in us, not a Third Person of a Trinity. This is in context just after Jesus says, "I will send another Comforter, . . . even the Spirit of truth" (John 14:16-18).