It means pushing yourself in a set until you absolutely, positively cannot do one more rep no matter how hard you try.

Negative failure is when after you reach normal failure, you have assistance in the positive and keep doing negatives until you can't control the weight on the way down.

Don't do this every single set, or you WILL overtrain. (Negative failure that is). There is a lot of debate about normal failure and overtraining....I think it depends on how your individual body reacts to it, and various other factors.

-LH