Taken from Variables for Weight Lifting and Exercise © 2003 Anthony Sell - All Rights Reserved
Some of my clients get frustrated when they innevitably get to a point in their workouts where they simply cannot finish a repetition of the exercise with the weight they have been lifting. This is considered the point of failure. I remind them often that this is a good thing. In fact, Weightlifting is quite possibly the only activity in the world where failure can equal success.
One of the best training habits to develop is to work the muscle to the point of momentary muscle failure. This means not only that you are unable to complete the repetition in question without the aid of a spotter, but that your muscle gives out in the middle of the repetition.
In this way, having pushed the muscle to the limit, the athlete is sure to have achieved their potential. This is also the fastest way to cause the body to begin a growth cycle.
The science then, is to determine exactly what weight and what number of repetitions it will take to get to that point in each set, for each exercise.
This is one reason why accurate records of your progress are so important (examples of which can be found here.). Unfortunately this is not an exact science, and what felt good one day, may be too heavy or too light the next. Many times, after enough experience in weightlifting, power lifters will go more by how they feel each workout, rather than what their last workout tells them to.