A bell boot or overreach boot is a plastic, leather or rubber boot that is placed around a horse's front hoof. (Almost always both feet).
The purpose is to prevent a common injury. Some horses, when ridden, are unable to get their front feet out of the way before their hind feet land in the same spot - this is caused by a fault in conformation or action. Additionally, when a horse lands from a jump, it's common for the hind feet to land very close to the front feet.
This can cause the horse to catch the back of a front foot with the toe of a hind foot, resulting in a "pocket" cut that's very likely to become infected and/or scar. Overreach scars are fairly distinctive and any horse that has one should be ridden in bell boots. Most horses, however, need them only for jumping.
Image modified by Nordlicht8 from photos from Maloq, via Wikimedia Commons.