Horseshoe
A curved band, usually of steel, fixed under the hoof wall to limit wear.
What it is for
A horseshoe protects the hoof's edge from wearing down too fast and can add grip, support or correction. The farrier shapes the shoe to fit the hoof, not the hoof to the shoe.
More detail
Horseshoes come in steel, aluminium and synthetic materials and in many shapes for sport, work or correction. They are usually fixed with nails through the insensitive hoof wall, or sometimes glued. Because the hoof keeps growing, shoes must be reset periodically by the farrier.
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Sources: British Horse Society · Merck Veterinary Manual.