A Miller (sometimes called an Outsider) is a role or role modifier such that the player passively returns an unfavorable result (i.e. Guilty) if investigated by a Cop.
For obvious reasons, standard Millers are Town.
Some moderators take the "passive guilt" concept to the point where Millers also investigate unfavorably to other roles (i.e. Gunsmith). Alternatively, specialized Millers can be created specifically for investigative roles other than Cop.
Sometimes, a Miller may be unaware of their Miller state -- that part of their role is hidden from them. This is used in some Open setups (like C9++) to prevent the Miller from functioning like a Named Townie. An unaware Miller in a closed setup is sometimes considered bastardly, though.
A rather controversial twist is the Death Miller, whose alignment is shown as "Mafia" by the Moderator upon death. This has been argued and discussed in as a source of distrust in the Moderator, which most people feel should not be tolerated. Thus, the Death Miller is an particularly scarcely-used role even in bastard mod games.
A Miller that knows they are a Miller and flips as such is considered Normal on mafiascum.net. A Miller returns a guilty result if investigated by a Cop, "Miller" if investigated by a Role Cop, and "non-Vanilla" to a Vanilla Cop.
Use and Balance
The foremost use of Millers is to weaken the power of a Cop. A Cop may prematurely claim with a guilty result upon the Miller, outting himself to the Mafia; or a Mafia member with a guilty result upon them may claim to be a Miller to avoid being lynched (though this doesn't usually work in practice).
Less commonly, a Miller may be put into a game without a Cop, as a red herring.
Self-aware Millers may also be considered Named Townies, as there is usually not more than one in a setup.
If you are a Miller, there are two schools of thought about optimal play:
The first school of thought is that you should claim immediately, ideally in your opening post. This ensures that the Cop will not waste an investigation on you. It becomes more likely that you will be lynched or shot by a Vigilante, however; otherwise, it would be too easy for Mafia to fakeclaim Miller as well.
The second school of thought is that you should not claim, but should play in such a way as to not get investigated; ideally, you would get yourself killed at Night. If investigated, however, you should expect to get lynched.