Aura beasts are monsters who can sense psi powers within individuals. They normally reside in 'the ether' an area just outside normal reality.
They are normally invisible but with 'break out of the ether' to attack the player. However, they might not sense you if you don't use psi-powers much.
They were summoned into the world by Nicolas Wrightson and appeared to be pulled back into their own dimension during his 'death'.