"You would be protected by an ancient magic of which he knows, which he despises, and which he has always, therefore, underestimated - to his cost. I am speaking, of course, of the fact that your mother died to save you. She gave you a lingering protection he never expected, a protection that flows in your veins to this day. I put my trust, therefore, in your mother's blood. I delivered you to her sister, her only remaining relative."
-- Dumbledore (OP37)
The old magic, also referred to as ancient magic, is magic which is not cast by wizards with wands. It is part of the “magical-ness” of the universe.
References from the canon
- Dumbledore's protections around Harry were connected through his mother's blood to his only living relatives, the Dursleys. (GF33,OP37)
- Lily's sacrifice of herself for Harry created a protection Voldemort could not break through. In fact, the sacrifice infused his skin with that love and Voldemort and Quirrell when under Voldemort's control couldn't even touch him. (PS17) Voldemort made a mistake by using some of Harry's blood to resurrect himself because it meant that while he could touch Harry without fear, he also couldn't kill him (GF32,DH35).
- "Dragons are extremely difficult to slay, owing to the ancient magic that imbues their thick hides, which none but the most powerful spells can penetrate." (GF20)