You can't breed wild horses in Minecraft. You can only breed tamed horses and both horses need to be tame to breed properly. So make sure you have tamed both.
Tamed and saddled horses can be used as a means of transportation in the game. When ridden, they are able to move faster and jump higher than a normal player.
The Horse Update is the name for Java Edition 1.6.1, a major update released on July 1, 2013. It added many new features such as horses, leads, coal blocks.