Lovers are a kind of "linked" role, in that their role abilities are intimately tied together. Lovers are two players who, when one dies, the other will die shortly thereafter, typically by suicide (ala Romeo and Juliet). Usually the lover pair are townies, often confirmed town to each other (thus becoming like suicidal masons). However, sometimes, one lover is otherwise a vanilla townie, while the other is a mafia goon. Thus the mafia don't want to kill the townie, since that would result in losing one of their own, but the townie likewise might not want to roleclaim, since killing the mafia lover will kill them as well. Typically lovers still win with their appropriate faction, so the town lover eventually has an incentive to roleclaim, even if it means them dying, because otherwise the town has no way to win. One way to fix this is to make the townie a power role, thus the townie would not claim so that the power can still be in the town (this is also known as siblings).
On rare occasions, the lovers will have their own alignment (lovers-aligned), making them a third party. The most common win condition, when this is the case, is to be alive at the end of the game (ala survivors). This has all the benefits and drawbacks of normal survivors, however. Another common win condition is to be the last ones standing (ala SKs), however this is often incredibly difficult.
Use lovers with care.