Warming up your horse is very important. You want to make sure he is relaxed and ready to begin working. Similar to humans, before horses run or do a lot of activity, they have to warm up in order to get their muscles loosened up to prevent further muscle injury.
When you warm up your horse, you get the chance to see what type of mood your horse is in, whether he's calm and relaxed, excited or stressed. Warming up your horse will allow you to determine what would be the best way to ride him, either with a long rein and a lot of leg, or with a short rein and not too much leg. Horses, just like humans, are a little different everyday depending on their mood. When you warm up your horse, you get him loosened up, which is very important, especially when jumping (as they are using many muscles).
When warming up your horse, you want to make sure you walk, trot, and canter your horse (all the three gates) to see if he's stiff at all or if your going to be having any kind of trouble during your ride.