In short eventing is a horse triathlon.
There are three phases that horse and rider can complete.
Phase 1: Dressage
Horse and rider must ride a prearranged standard test in a small ring. They typically show all three gaits (walk, trot, and canter) and perform figures such as circles. This is the only phase that is judged subjectively. It is judged on accuracy and how well you and your horse work together.
Phase 2: Cross Country
Horse and rider jump a course of fences over varied terrain. Teams are penalized for failing to jump a jump on the first try and for being outside of the time. Cross-country courses are typically rather long compared to a show jumping or hunter course. Horses jump these courses with quite a bit of speed. The fences do not fall down. It is the most dangerous phase in the sense that if you make a mistake it can be very painful. This phase tests the team’s bravery and endurance.
Phase 3: Show Jumping
Horse and rider jump a course of fences in a ring. Teams are penalized for failing to jump a jump on the first try, knocking a fence down, and for being outside the time. The courses are in a smaller area so there are more turns and the fences will fall down if you hit them. This phase tests how well your horse jumps and how well you can turn.
That is the typical format for a three-day event.
Horse Trials are very similar but they are lower level and they have show jumping before cross-country. It’s safer that way because if you are out of control show jumping you won’t be safe cross-country so the show officials can stop you before a bigger problem occurs.