I know how much I am normally able to lift each exercise. So let's say 125 lbs shoulder press, I expect to be able to lift the weights 10 times the first set, 9 times the second, 8 the third set. If I can't lift the weights 10 times I failed early.
Basically failing to lift weights that you could lift say last week. There are other factors too of course like fatigue, food, etc. that can make you fail to lift the same weights.