In the United States, a Hare & Hound is a type of off-road racing event where the entrants compete on dirt bikes over a marked course of natural rugged terrain. Hare and Hounds events are made up of two separate race courses with each course averaging 40 miles in length. The break between each course (or loop) is used for refueling and bike maintenance. The first racer to cross the finish line after the second "loop" is considered the winner of the event. Hare and Hounds are typically held in the desertic regions of California, Nevada, and Idaho.
A Hare & Hound is different from a Hare Scramble because it does not repeat the same loop twice. Pre-running the course is not allowed, and many sections are brand new, so that the first rider only has a series of arrowed stakes to lead the way, making that person the "hare" and everyone else is the "hound" following the newly-created path. It is a start-to-finish race, so the midpoint pitstop is made as quickly as possible in order to minimize downtime.
In the United Kingdom, A Hare and Hound (H&H) is a type of off road motorcycle sport where the entrants compete motorcycles over a marked course of natural rugged terrain. The event is comparable to an extended length motocross (anything from 1 hour to 12 hours in extreme examples) but tend not to included artificial jumps that characterise modern motocross. The general length of a Hare and Hounds tracks is around 6 miles although it does vary depending on the status and club which the track has been made for.
For more information see the enduro article