Adventure Racing takes on many forms (expedition, sprint, short, urban, etc.). It is usually a team sport but is not a relay. Co-ed teams of three or four race other teams over a course that usually includes trekking/trail running, mountain biking, orienteering (map & compass), paddling and some type of rope work (climbing). The order will differ with each race and the course is kept secret before the start. For a team to place in a race they have to stay together (within 100 feet usually) throughout the race.
Some races add in special events along the course which can be mental or physical tests. (The last race that I helped organize was won at the finish line by the team that finished a puzzle fastest. It was fun watching them try to figure it out after 8-10 hours of racing.) Other disciplines have been added in some races including swimming, rollerblading, scooters and snowshoeing.
Here is an article that might help you understand how it started.
History of Adventure Racing