A person, especially a member or follower of the Beat Generation, whose behavior, views, and often style of dress are pointedly unconventional.
I think the term applied originally to fans of beat poetry. According to Merriam-Webster: Main Entry: beat·nik Pronunciation: 'bEt-nik Function: noun Etymology: [3]beat + -nik Date: 1958 : a person who rejects the mores of established society (as by dressing and behaving unconventionally) and indulges in exotic philosophizing and self-expression