Just what is Cross-Country?  It is most often seen in Three-Day Eventing.  The history of which can be found HERE.

Cross Country is the phase that sets eventing apart from all other types of equestrian sports. The horse and rider must complete a set of solid jumps over natural terrain, often through water, over ditches and very uneven ground. This phase is truly a test of the horses' bravery, endurance and speed, and involves a close bond between the rider and the horse. Cross-country is perhaps the most demanding event as horse and rider must rapidly negotiate jumps and obstacles over fields and through woods to complete the course within a set amount of time. It may also be the most thrilling for competitors as they "walk the course" while rider and horse speed by in close proximity!