Creatures that are dueling each other are spiritually linked to each other in a state that's slightly out of phase with everyone else. This doesn't have any inherent mechanical effects in and of itself, but it implies a structure for how those creatures interact with each other and the world around them that may be interacted with by duel modifying effects or other abilities. The term "in a duel" is often used to refer to a creature that is dueling. This does not mean that the "duel" must have been started by Duel.
If a creature that is dueling becomes incapacitated or attacks a creature that they are not dueling, this creature is considered to have "lost the duel". This also ends the dueling condition for that creature. If a creature is ever the only one remaining in a given duel, the duel ends and they are considered to have "won the duel".
Duels typically have a "range" of 30 feet. This means that if any creature that is dueling Moves more than 30 feet away from any other creature that they are dueling with, they are considered to have "lost the duel".
The dueling state is not visible in the Material Realm, but there is a very slight tether that can be seen in the Ethereal Realm. There are no restrictions on what realm a duel can take place in, but all participants must be within the same realm. Any participant that leaves that realm is considered to have gone out of range and therefore "lost the duel".