"Make your upper back tight" , "make your glutes tight" and so on are often intrusctions given on how to do various exercises in the gym... but why actually do we do this?
Case 1: Voluntary tightening of muscles around joints that should remain in a fixed angle throughout the movement
This is commonly seen in lifts where the load is transmitted through the torso, which ideally remains rigid throughout the movement. E.g. The squat, deadlift, rows, etc. In these lifts, if there were no muscular tension in the back, it would go limp, bend forwards, and you wouldn't be able to complete the lift.
Now, as gravity is tending to pull the torso into flexion (bending forwards) during these exercises, it might conceivably be possible for the extensor muscles of the back to resist that, however due to the large number of joints in the spine, the degree of control that would be necessary to achieve that just isn't possible. So instead we tense up everything around the core, including the spinal flexors (the abs), and with the opposing spinal flexor and extensor muscles pulling against each other, everything just gets locked into position and has a good capacity for resisting movement caused by external forces.
A related case is the legs and back during the bench press, where the load is not actually transmitted through these body parts (since the loading in the bench press is only through the arms to the shoulder blades), but where these muscles remain tensioned in order to hold a favourable body position, i.e. the arch.
So in these cases, we need to voluntarily maintain tension in certain groups of muscles in order to maintain a position necessary for the exercise.
Case 2: Voluntary tightening of muscles that are supposed to be working, involving joints whose angles should be changing throughout the movement
You'll often hear trainers cueing their clients to "squeeze" the target muscle during an exercise, e.g. squeezing the glutes during a deadlift or hip thrust. The believe is that this ensures that the target muscle is "activated", which comes from a mistaken belief that the glutes could somehow fail to activate during a deadlift, whereas in reality, the glutes are definitely already active, regardless of whether you can feel them, and squeezing them further is actually just tensioning the muscles that perform the opposite movement. When you "flex" a muscle, you're contracting both the target muscle and its antagonist muscle to pull against each other so that no joint movement actually occurs. E.g. When you flex your biceps, you are simultaneously applying the same amount of tension to the triceps, so that no movement occurs. Hence, when you attempt to "squeeze" the glutes during a deadlift, you are actually tensioning the hip flexors to fight against the glutes, which can only be detrimental to your lifting performance.
Deliberately focussing on keeping the target muscles "tight" like this is not a good idea.
When doing hanging work like leg raises, keeping your shoulders tight is in fact very important for your rotator cuff. These muscles aren't equipped to hold the shoulder joint together, so you'll have to do that with the chest and upper back muscles. Otherwise, you'll either irritate the whole joint area, leading to inflammation or outright pop the shoulder joint.