The wraps put pressure on the leg to decrease swelling and increase circulation. It is a good idea to put them on a horse that will be put in a stall after intense work because their legs can swell up and get stiff. The wraps also support the tendons. Beneath the wraps i put a linement or a mix of which hazel and rubbing alcohol. This helps so th and cool the strained tendons and ligaments, and also decreases swelling.
Also some horses get swelling from being stabled and therefore bandage a prevent this. They often get the swelling of they cannot move around much in a stable so ponies are often fine but bigger horses suffer sometimes. Also I know a few people that do it if their horses have socks at a show so they stay cleaner overnight and less of a haste in the mornings.