Antlers and horns are two different things. Horns are permanent and grow larger each year, they never fall off except as the result of injury. Antlers grow too, they grow faster than horns and are shed yearly.
In a male deers first year of life structures known as pedicles form on his forehead. These will be permanent and will be the base on which the antlers grow, and later will be the point they break off.
The following year, his yearling year, he grows straight spike shaped antlers. Every year after that the rate of growth is expedited, with a bigger set of antlers grown and shed yearly. In most species of deer each year means a new branch is added to his set of antlers.
The new antlers are covered with a soft, blood rich, layer, called velvet. This layer provides the oxygen and nutrients needed to grow the antlers. When the antler is reached its full size, a ring in the velvet around the base of the antler forms, cutting off blood supply and the velvet begins to fall off, or is itched off. A dry bone antler is revealed underneath.
Antlers are grown every year for the same reason. The rut. The mating season. The chance to impress females and to drive away other males. A male deer with a larger set of antlers is often the winner of competitions. These fights are not death matches, although occasionally two male deer will become intertwined while fighting and sometimes will die with their antlers tangled together. Males who win fights, get the prize, a chance to build a harem of females and breed with them.
Antlers have also been shown to have an effect on an animals hearing. The bigger the antlers, the better the hearing. Possibly this aids the deer when seeking mates, or to find rival males.
Because the antlers are not needed after rutting and mating season, they are shed, typically through the winter. Dropping testosterone levels in a male deer trigger the antlers to fall off. A new set of antlers then begins to grow, being larger than the previous set.
In most deer species, and moose, only the males grow antlers, in reindeer, females also grow antlers, which they shed in the summer.
Another interesting note is that if a male animal, such as a moose is castrated, it will shed its current antlers, and grow an awkward set of deformed antlers, known as Devils antlers, and these will never be shed, nor will they be as large as a normal set of antlers.