In short : Horseshoes are used to protect the animal's hooves from wear and tear.
More detailed :
http://en.wikipedia.org/wiki/Horseshoe
HISTORICAL DEVELOPMENT OF THE HORSESHOE:
http://www.gutenberg.org/catalog/world/readfile?fk_files=168587&pageno=23
Horseshoeing, very likely, was invented by different nations at about the same period during the migration of the nations, and the various kinds of new inventions were brought together in Germany only, after each had acquired a national stamp according to climate and usefulness. Reasons for use Since the early history of the domestication and use of horses, many factors have contributed to the need for the bottoms of domestic horses' feet (hooves) to have additional protection over and above their natural hardness. Less healthy food Live grasses, weeds and shrubs, which are eaten in the wild, are high in nutrients such as beta carotene. Cultivated feeds lose a high proportion of their carotene within hours of harvesting and so do not provide this vital ingredient to the horse. The hoof is made of horn, much as the human fingernail, and grows hard, tough and flexible only with optimal nutrition. Furthermore, domestic horses are often fed grains and other concentrates as well as alfalfa and lush pasture, all of which are known to cause laminitis, inflammation of the laminar attachments of the foot which holds the hoof wall onto the underlying coffin bone. This unhealthy and unnatural diet, when it doesn't cause acute laminitis, contributes to weak feet because the horn is attached to the coffin bone by only a weak attachment. Effectively, a diet which is high in grains, legumes, or lush pasture causes sub-clinical laminitis. Because horse shoes hold the hoof wall in a rigid shape they can reduce (but not eliminate) the pulling away of hoof wall with weak laminar attachments. Less varied terrain Horseshoes are not needed in nature as the horse walks and grazes continuously over a wide variety of surfaces. The consequence of this nonstop travel on the horse's feet is to keep them worn to a small, smooth, even and hard state. The continual stimulation and irritation of the sole of the foot keeps it thick and hard, much like a callus. However, in domestication, the customary amount of ground covered by a horse on a daily basis is greatly reduced. Therefore, the hooves harden much less and are more vulnerable to injury. Added weight Horses' hooves can become quite worn out when subjected to the added weight/stress of a human, pack loads, cart or wagon traces. Wetter climate Horses have moved from the more arid steppes to the wetter climate of northern Europe. This wetter climate and heavy soils softened the hooves and made them prone to splitting, making hoof protection necessary, and consequently it was in northern Europe that the first practical horseshoe arose. Exposure to ammonia The hooves of horses that are kept in stalls or small turnouts are constantly exposed to ammonia from urine. The hoof capsule is mostly made from keratin, a protein, and is weakened by this exposure. Wearing shoes does not prevent or reduce damage from ammonia exposure. Rather, they are meant to reduce wear on weakened hooves. Consequences of less healthy hooves In captivity, absent the natural conditioning factors present in the wild, the feet of horses grow overly large, long, fragile and soft. Hence, protection from rocks, pebbles and hard, uneven surfaces is lacking. Cracks in overgrown and overly brittle hoof walls are a constant danger, as is bruising of the soft tissues within the foot because of inadequately thick and hard sole material. Corrective shoeing The shape, weight, and thickness of a horseshoe can significantly affect the horse's gait. Farriers trained in hot shoeing can make custom shoes to help horses with bone or musculature problems in their legs. The horseshoe seems to have been introduced to Western culture by the Greeks in the 4th Century.