Priming Is Not a Warm-Up
A warm-up raises tissue temperature and gets blood moving. Useful, and it is not the same job as priming.
Priming decides which muscles are switched on when the first real rep starts. You can be perfectly warm and still walk into a session with a glute that is not going to contribute, and if it is not contributing in the warm-up it is not going to start contributing under load.
Why a muscle needs waking up
Muscles get quiet. A hip that has been sitting in a car or a classroom for six hours, or a shoulder that has been guarding a sore spot for two weeks, stops being recruited properly. The nervous system finds another way to get the movement done and stops asking.
Then you load it. The pattern that runs is the compensated one, because that is the pattern that is currently available, and now you are adding weight to it.
Priming is the step that makes the right muscles available before that happens.
Where it starts
The hips and the spine, almost always.
Force moves through you as a chain, and the hips and spine are the middle of it. Everything above and below routes through there. A shoulder problem is often a thoracic spine that will not rotate. A knee problem is often a hip that will not stabilise. Priming from the middle out means the rest of the chain has something to work against.
What it looks like
Short. Specific. Five to ten minutes of movements chosen because of what is quiet on you, not off a list.
Band-assisted bridges to get the hips and the spine talking. Shoulder work to open the thoracic spine and anchor the scapula. Adductor and VMO work before anything asks the knee to control rotation.
None of it is hard. That is the point. You are not trying to fatigue anything, you are telling it to be present.
What changes
Less energy leaks. Muscles that were being covered for start doing their own share, and movement gets cheaper. Power comes out faster because the chain is connected rather than being assembled mid-rep.
And the session is safer, because the reps you are about to do are being run by the muscles that were supposed to run them.