The word "Anarchist" is used with very different meanings depending upon who is talking. merriam-webster.com says "1) a person who rebels against any authority, established order, or ruling power. [That could be any teenager.] 2) one who uses violent means to overthrow the established order." That description could include George Washington, the Tea Party, as well as Che Guevara. It could also mean meatheads that get a thrill out of provoking a riot. I've noticed plants from White Supremacist camps who are charged with provoking a riot; these are also included in the definition of anarchist.
But there are also non-violent Anarchists, who advocate the reduction of central government influence, and increased local control of government, by non-violent means. Non-violent anarchist used to be #3 in the dictionary meanings, but seems to have been purged. Often those from Europe and South America understand this aspect of Anarchism.
In other words, Anarchism is when the People take control of the government whether it be through violent means or by non-violent means. If this is true, then Anarchism may be the only true Democracy!.