False Roles are roles that claim to have some ability, but the ability does nothing.
A False role appears as a regular version of the role in a player's role PM, but actually has no effect. They are activated the same way as the original role, e.g. passive False roles do nothing at all, untargeted active False roles can be activated to no effect, targeted False roles can be targeted but do nothing to their targets. (This last category is equivalent to Visitor).
The False modifier is by default visible in Rolecop reports, making it possible to determine what is happening, and will in any case show up in the flip.
Some moderators will not even consider who a player with a false role targets. If a false Tracker targets someone, the moderator will simply disregard it.
A False Inventor is a variant that is actually an Inventor, but its Inventions do nothing (whereas an Inventor with the False modifier would fail to even give out the inventions, a False Inventor will give out False roles as inventions). Some moderators have even taken this concept to mean an Inventor who gives Inventions that claim to do something, but actually do something else (usually much worse).
False should never be used on win conditions; for example, a False Condemner would be incapable of winning, effectively making the game pointless. This goes a step beyond even regular bastard modding.
A Vanillaiser effectively causes other players' roles to become False.
The opposite of a False role is a Hidden role (which does actually do something, but which claims to do nothing).
Use & Balance
There is essentially no argument that False roles are firmly in the realm of bastard modding.
Obviously false roles are less powerful than real ones, but they also have a nasty tendency to get their bearers eliminated via Eliminate All Liars.
It's rare to become aware that you have a False role, so it's a hard role to play in an informed manner. If you're playing a bastard game, and have received no result more often than seems reasonable, it's a possible explanation; nonetheless, it's probably best to continue trying to use your role in case the true explanation is something different, as attempts to use a False role, whilst futile, are hardly likely to have negative consequences.