In chemistry, a radical (more precisely, a free radical) is an atom, molecule, or ion that has unpaired valency electrons. With some exceptions, these unpaired electrons make free radicals highly chemically reactive towards other substances, or even towards themselves
"Free Radical" has been used titles of songs, publications, films, band names, and other places metaphorically because both "free and "radical" have meanings independently that combine with the idea of "highly reactive" from the phrase. Radical can mean a person favoring drastic political, economic, or social reforms and free can mean both"acting without self-restraint or reserve" and "unrestricted by authority or rules".
So all together, when referring to a person, it has the idea of someone who has a radical philosophy, is free from the constraints of authority or social norms, and causes a lot of reactions with other people (although whether those are positive or negative depends on your views). A free radical is a different idea from just a radical, because some people with radical philosophies might still be restricted by some authority or set of rules.
Describing someone as a radical has a negative connotation currently because it's widely used to describe terrorists, and adding "free" to radical causes a different, less negative association. My impression of a free radical is a person who is more likely to act and think independently (not willing to take or give orders) and less likely to be violent than someone who is just a radical.