One with a more extreme point of view than the mainstream. Radicals are more ideological than moderates. Radical opinion can appear to be hardcore and at times even anti–popular.
Radical can also be a description for an event or special thing. A modification can be radical such as changes to a law or the change in appearance of a program with the use of skins.
A radical can be anywhere within the political spectrum, though generally they are found at the extremes of full economic freedom (free trade), full economic control by the state (socialism), full social freedom (anarchism), full social/economic control (authoritarianism) / fascism).
An interesting online test can place you on the “political compass”.
TakeDown.NET -> “Radical”