A nihilistic person believes that life is meaningless. If you go through your teenage years in a nihilistic frame of mind, nothing seems to matter to you.
Someone who's nihilistic believes in the philosophy of nihilism, which embraces the idea that life as we know it is useless. If you're nihilistic, you don't believe in anything — not religion, a moral code, love. Being nihilistic is also closely related to the political philosophy of anarchism, a belief that all social structures need to be destroyed before a new, better society can be developed.