There are essentially three types of “genders” of horses – mares, stallions, and geldings. It is important to know these differences especially when deciding what gender of horse you need.
TL;DR: Stallions are male horses. Mares are female horses, and geldings are castrated male horses.
Mares are rarely spayed like dogs and cats are, first because it is a complicated surgical procedure and second because it is not necessary. Almost all mares are easy to take care of and are very rideable. It also enables owners to breed a mare if they choose to do so.
A stallion is almost always kept a stallion for breeding purposes. For example, top winning racehorses might end their racing careers early to begin a breeding career in order to continue top performance lines; a top show jumper may also be kept a stallion while continuing their jumping career.
Unlike mares, stallions can be difficult to handle and if not handled appropriately can put other horses and people in danger. Stallions have a strong breeding instinct. As a result, they will fight other stallions and geldings to be the dominant horse in a herd. This behavior can include rearing, biting, kicking, and striking out with their front legs. Keep in mind that a horse usually weighs a thousand pounds or more. It is near impossible for someone to control a highly energized stallion safely.
A gelding is a stallion that has been castrated. Unlike spaying a mare, castrating or gelding a stallion is a fairly straightforward procedure. Veterinarians recommend that a male horse be gelded between the ages of three months and one year. After a year, testosterone levels are such that the horse’s behavior is impacted so that it is more stallion–like. Once a male horse is gelded, it becomes easier to train, ride, and handle.
Not all mares are mare-ish, not all stallions exhibit aggressive behavior, and not all geldings are perfectly behaved. However, knowing the general tendencies of each “gender” will greatly help you to decide what kind of horse best meets your needs.