The manual has answers to this; I don't know if it's mentioned in game at all.
The Aard Sign - A telekinetic wave that can throw back, knock down or stun an opponent. This Sign can also be used to destroy obstacles, for examplle crumbling walls.
The Yrden Sign - a magical trap placed on the ground, which will wound and immobilize opponents. The Sign's basic level allows you to place a single Yrden Sign on the ground. After upgradin it, you'll be able to place up to three Yrden Signs at a time. These will work in unison, creating an impassable barrier.
The Igni Sign - a gush of flames that wound opponents. When upgraded, the Sign has a chance of incinerating opponents and has a larger area of effect.
The Quen Sign - a protective shield that lasts for 30 seconds at the Sign's basic level. It is a Sign that Geralt uses on himself - the Quen absorbs all damage directed at you, and the upgraded version reflects 50% of the damage at the enemy. While the Quen is in effect, Geralt cannot regenerate vigor.
The Axii Sign - a charm placed on an opponent. If the charm attempt is successful, the enemy will become your ally for a short while, fighting at your side.