They help protect your horse from tendon damage or if it's leg hits a jump or even helps prevent injuries
SMB (sport medicine boots) also help absorb shock and can help with preventing hyperextension of the fetlock (which lessens the chance of pulled tendons and suspensory ligaments).
Support and protection for your horses legs.
They essentially just add support for horses legs. (They are fairly fragile and a leg injury could be career ending) They also add protection against things hitting them such as their own hooves, and poles if you are jumping. However if you plan on showing your horse shouldnt wear any sort of boots if doing hunter classes.
It depends on the boot. I use splint boots/sport boots because they support the tendons and also prevent damage from objects (hooves) hitting the leg. If you don't worry about support, brushing boots or polo wraps work well