The Condemner is a third-party role whose win condition is to get a specific person (the Condemnee) voted out, or eliminated. If the Condemnee is eliminated while the Condemner is alive and on the Condemnee's wagon, the Condemner wins. If the Condemner dies first or the Condemner is the only scum left in the game and the Condemnee is still alive, the Condemner loses.
Mods have differing policies in regard to what happens if a Condemnee is nightkilled: the Condemner may gain the pro-Town Win Condition, may become a Survivor, may change their Condemnee to whoever made that kill, or may win as if that player had gotten eliminated. This decision is made based on game balance and role mechanics. However, the third option is a poor one from a balance perspective - the Condemner in that position can simply claim Watcher with an incriminating result on that player. Since the player that killed the previous Condemnee is more than likely scum, everyone wins (except the scum).
In most games, if the Condemner succeeds in fulfilling their Win Condition, they will leave the game and in the end be pronounced a joint winner with whichever faction wins the main game.
In themed games, Condemners may have more than one Condemnee. If this happens, it is not necessarily the case that the Condemner has to be directly involved with each Condemnee's death.
In some themed games, Condemners are not told who explicitly they must kill, but rather the flavor names of their Condemnees. While this is frowned upon - the Condemner can't know which players have those flavor names, and is thus directionless - it is sometimes necessary to preserve the integrity of the game (i.e. if one of the Condemnees is scum).
The Condemner Win Condition may be in addition to a factional Win Condition - for instance, a Mafioso may win with scum IF a particular player does not live to endgame. See also Usurper.
If there are multiple Condemners in the game, as a general rule they are Condemnees for each other.
Use and Power
Condemner should be balanced like a guaranteed elimination on the Condemnee, whatever the Condemnee's alignment is.
In the case of a Condemner with multiple Condemnees - especially if the Condemner is not told the identities of who these Condemnees are - the Condemner's power is more on par with a Survivor.
On Day 2, claim Cop with a guilty result on your target. By the time they figure out you're lying, you will have already won.
If this causes the real Cop to counterclaim, you're probably best off immediately claiming Condemner and hoping the Town helps you out just to get you out of the picture.