The gear that people put on horses to control them - from halters to harnesses. Whole books have been written about tack. When mankind first tamed the horse thousands of years ago, the only equipment was a leather thong wrapped around the horse's jaw. Native Americans rode that way for centuries. The basic bridle as we know it was developed by the Egyptians more than 400 years ago. Today, a bewildering number of options are available to the rider.
The two basic styles of riding, English and Western, use quite different saddles and sometimes very different bridles. For either style, the average rider will use the following: a bridle with reins and a bit (or a bridle without a bit, called a hackamore); a saddle pad; and a saddle with a cinch or girth, stirrups, and stirrup leathers. Some horses also need a martingale, which offers further control of the head.
When shopping for tack, make sure it fits your horse and fits you. There are options for all budgets, from finding a good, used saddle in your local tack shop to custom-ordering a fancy dressage saddle. Well-made used tack is often a better bargain than new, cheap equipment that might not last as well. Don't be shy about seeking help when purchasing tack - it's a big investment and is worth doing right.