The Cult is a third-party group that seeks to recruit players into itself. The recruitment is done by a Cult Leader who is typically the only member of the Cult at the beginning of the game. At Night, it can recruit players into the Cult; these players henceforth lose their previous role identities and become Cultists. The Cult wins when it comprises half of the player list, at which time it controls the lynch and trivializes the rest of the game.
Cultists usually do not have the ability to recruit players, so if the Cult Leader dies, the Cultists are defenseless but must survive until they attain a majority. This can be difficult to do, especially if the Cult Leader only lives long enough to recruit one Cultist.
A common variation of Cult causes all of the Cultists to suicide if the Cult Leader dies. This is to prevent orphaned lone Cultists, but the necessity of this rule is disputed.
Some moderators allow Cultists to recruit players if the Cult Leader dies. However, this becomes completely impossible to balance, as there is virtually no chance of the Cult ever being completely wiped out.
Moderators are mixed in regards to what happens if a Cult Leader attempts to recruit Mafia, as a recruited Mafia player can simply tell the rest of the cult who the other scum are. Options have ranged from the Mafioso simply not getting recruited, to the Cult Leader dying, to the Mafioso getting recruited and replaced at the same time (so that they don't know who the other scum are). The most common solution is usually the second one.
Use and Power
If the Cult is not exterminated within the first two game Days, they almost inevitably win. Therefore, you shouldn't use these unless other people have told you you know what you are doing.
Most attempts at balancing a Cult need to address two problems: a swing issue (in which killing the Cult Leader early makes the Cult a non-issue, but failing to do so leaves them very powerful), and the issue that the cult can typically recruit as fast (or faster) than the town can lynch them. Balanced games containing a Cult nearly always need to have some means of slowing the Cult down. This is much easier to do via a change to the game mechanics (or to the Cult mechanics) than it is using power roles; although roles like Alarmist help, they come nowhere close to the amount of power needed to keep the Cult in check.
Cults have been criticized for being very hard to balance. For example, the Town could lynch Cultists each Day but still lose because someone else becomes recruited to take their spot. Cults could also overpower the town if they recruit all of the Town's power roles. Most players also find it annoying if a Cult Leader targets a member of the Mafia on the first night if the suicide-on-scum-recruitment rule is used.
Another criticism of Cults is that they can make a player's previous efforts in the game pointless due to formerly pro-Town players (either themselves or others) suddenly becoming scum. This criticism is common to all alignment-changing roles.