A group that's described as being paramilitary resembles an organized army. During the American Revolutionary War, the minutemen were a paramilitary group that fought in the earliest battles.
When civilians organize themselves (or are organized) into a group that appears to be military, or that assists actual military troops, that's a paramilitary organization. You can also call it, simply, a paramilitary. The early twentieth century word combines the prefix para-, "near" or "resembling," and military, from its Latin root militaris, "of soldiers or war."