Just to confirm the accepted answer, I link here relevant definitions from Springer Online Encyclopaedia of Mathematics (definitely more reliable source than MathWorld and even PlanetMath...):

Nilpotent algebra

Locally nilpotent algebra

Nil algebra

So the most appropriate thing to say would be "the augmentation ideal is nilpotent". This terminology is very standard.

Just to confirm the accepted answer, I link here relevant definitions from Springer Online Encyclopaedia of Mathematics (definitely more reliable source than MathWorld and even PlanetMath...):

Nilpotent algebra

Locally nilpotent algebra

Nil algebra

So the most appropriate thing to say would be "the augmentation ideal is nilpotent". This terminology is very standard.