Anything offbeat is quirky or unusual. An offbeat hair color like magenta will definitely stand out in a crowd of blonds, brunettes, and redheads.
This informal adjective is a much more admiring way to say "weird" or "freaky." If your aunt's style isn't like anyone else's, and you love that about her, you can describe her as offbeat. If you love unusual humor and unconventional perspectives, you probably also enjoy offbeat movies and books. Since about 1938, this has been the primary meaning of the word, but earlier it meant "music that doesn't match the beat."