The reason knee wraps are so highly valued by power lifters is that they allow more weight to be lifted in the squat. How? During the eccentric (downwards) phase of the squat, the tightness of the wraps allow for a high amount of elastic energy to be stored, which can subsequently be released during the concentric (upwards) phase—resulting in heavier and faster squats.
Furthermore, knee wraps are believed to reduce stress and pulling forces on the quadricep tendon, which is attached to the quadriceps and the patella (the kneecap). When you squat, the tendon pulls on the patella. Reducing the stress on the tendon helps to avoid detaching your tendon from the patella, or tearing your quads altogether, which are both pretty nasty injuries. When you consider the monster weights that competitive power lifters move in the squat, it makes sense why power lifters choose to squat with knee wraps.
While knee wraps do allow you to move more weight, they don’t necessarily help you get any stronger. This is because they are restrictive in nature, and because they completely cover the patella and are worn tightly (thus pushing the kneecap into the thighbone), they can increase the friction between the patella and the cartilage of the kneecap. As you might expect, this can lead to injury and troublesome knee joint problems like arthritis