Extremism is a political or religious philosophy that's very far from the mainstream. Because it's so different from the average person's politics. being an anarchist is often considered extremism.
When someone's beliefs are considered to be extreme by most people — if they think, for example, that people should be executed for eating certain foods or using certain words — that person is said to practice extremism, and is labelled an extremist. These words are almost always used in a derogatory way, by people who see themselves as centrist or moderate. The Latin root is extremus, "outermost" or "farthest."