Endurance riding is a challenging sport. Most states have local chapters of the AERC, or regional endurance-riding clubs and organizations. If you've never done it, my experience of endurance-riding horsefolk is that they're welcoming, helpful, and will bend over backwards to answer beginner questions, and encourage you and your horse safely through your own first endurance-riding experience. And there's a lot to learn.
Essentially, an endurance ride is a marathon on horseback. The usual distances vary from 25 miles (limited distance) all the way up to 50, 75, or 100 miles. There are multi-day rides, as well, for those horses and riders who just can't get enough. If that first 50 miles doesn't satisfy you, you can ride another 50 tomorrow, too.
If, however, you're finding yourself a little bored with an eight or ten mile trail ride, two or three times a week, and it seems like fun to ride further, this might be a sport for you to explore. You can start on the American Endurance Ride Conference website, where they list the AERC-sanctioned rides in your area. It's important, by the way, to choose a sanctioned ride, as opposed to a non-AERC sanctioned ride. The organization works very hard to keep horses and riders safe, prevent accidents, injuries, and provide oversight for this demanding and challenging sport.
This is an extreme sport, and not for every horse and rider team. You should discuss the possibility with your horse vet, and probably with your own doctor, if it's something you think you'd like to try.

