What is muscle failure (the point of failure)?

In one line

Muscle failure is the moment in a set when, despite trying, you cannot lift the weight one more time with proper form.

What is muscle failure (the point of failure)?
The 'failure' in 'one set to failure'
In workout plans and gym talk you hear 'go to failure' or 'do it until you fail'. Here, failure does not mean you did something wrong. It means a certain 'point' you reach within a set. This post explains exactly where that point is and what happens in the muscle at that moment.
In short
The moment you cannot lift once more with good form
Muscle failure is the moment in a set when, despite trying, you cannot lift the weight one more time with proper form. People often just call it 'failure'. It is the same point that the RPE and RIR post called 'failure'.
First, reps and sets
One lift is 1 rep, a group is 1 set
Lifting a weight up and lowering it once is called a 'repetition' (rep). A group of reps done in a row without resting is called a 'set'. Failure comes within a set, when you keep doing reps until you can no longer lift the weight.
Why 'failure'?
The moment the lift does not go as intended
A dictionary defines failure as something not turning out as intended. In muscle failure, you try to lift the weight, but it does not go up as intended. The muscle has become too tired to lift that weight again.
The exact standard
If your form breaks, you have already failed
Researchers define failure strictly. If you cannot complete the lifting part through the full range of movement without changing the set form, that is failure. If you can only get the weight up by swinging your body or lifting it halfway, you have already passed the point of failure.
As failure gets close
The weight goes up more and more slowly
The first rep of a set goes up quickly, but as reps add up, the same weight rises more and more slowly. When people did the bench press as fast as they could until failure, lifting speed fell to less than half of where it started. So the lifting speed tells you fairly accurately how many reps are left before failure.
The muscle works harder
More muscle fibers join in near failure
A muscle is made of long, thin cells called 'muscle fibers', bundled together. The body uses only as many fibers as it needs, and as a set gets closer to failure, more and more fibers join in. In fact, during the last reps, the electrical signal a muscle gives off when it works grew stronger while lifting.
Failure comes in the lifting part
The lowering part tires less
Failure comes first in the part where you lift the weight. In the same set, the lowering speed slowed down much less than the lifting speed. Also, right after failure, you can keep lifting at once if you reduce the weight, which is exactly what a drop set does.
Something to watch
Form breaks down more easily as you tire
The American College of Sports Medicine has stated that lifting to failure is not suitable for some people, such as older adults. The reasons are strain on blood vessel health and a higher risk of injury when tiredness breaks down form.
A common misconception
Do you have to reach failure for muscles to grow?
No. Compared with training that stopped before failure, training to failure did not grow muscle more. Still, muscles grew less when sets were stopped far from failure. The key is not 'all the way' but 'close'.
Summary
The moment you cannot lift once more with good form
Muscle failure is the moment when, despite trying, you cannot lift the weight one more time with proper form. To build muscle you do not have to go all the way to failure; getting close to it is the key. Related terms: RPE and RIR, drop sets, rest-pause.