Extremism is a catch-all term for those whose political or religious views are far from the center of a given political spectrum, with connotations of being dangerously so. It is often synonymous with wingnut. It also refers to both wingnuts and moonbats simultaneously, given that "wingnut" is sometimes specific to the far right and "moonbat" specific to the far left.
More specifically, it has been used to refer to those wingnuts and moonbats who have an "end justifies the means" mentality and are willing to use violence or other extralegal means to achieve their goals. However, it is sometimes also used to imply that said wingnuts and moonbats are criminal elements willing to use violence even when in some cases they are not.
Wingnuts and moonbats usually don't like being called extremists, although they'll happily call each other extremists. Then again they usually don't like being called wingnuts and moonbats, either.
One of the early and still insightful treatments of the subject is Eric Hoffer's 1951 book "The True Believer." Check it out (as in at your local library).