There are many reasons horse's legs are wrapped and there are many different types of wraps and boots. Some wraps are meant to support, protect, or simply to hold on a bandage or icepack when a horse is injured. Wraps can also be used to ship horses. When a horse travels its legs will be wrapped to prevent being injured during the journey.
Different types of boots are made to support/protect in different ways and some are made to support/protect different areas of a horse's leg. You'll see splint and sport boots on a horse that's doing a high-impact sport like jumping or racing. Skid boots may be found on a reiner or a barrel racer to keep the horse from skinning the back of its legs when it skids to a stop. Bell boots go over a horse's hooves to keep the backs of them from getting knicked and cut when a horse does something called "overreaching". Overreaching is when a horse's hind hoof reaches so far forward that it hits the front heel. It also protects from "knocking", which is when a horse's legs are set close together and tend to hit each other in passing.
There are also boots that go over the knee and hock joints that are simply meant to support the joints.