One who does not follow the norms of their overall society or culture.
The irony of one who claims to be a nonconformist is that they do conform to their society or culture to some extent. For example, unless he or she made up a language only he or she knows, he or she do share the same language with others in his or her culture or society, and therefore he or she is a conformist in that respect.
If one to were to learn a bit about modern psychology
, he or she would discover that nonconformists are almost nonexistent.
Lindsay: Think for yourself.
Elise: I won't follow your advice. I won't "think for myself." I am a nonconformist.