Someone who's unaccomplished isn't particularly skillful — at least, not yet. An unaccomplished nine-year-old trombone player may eventually become a virtuoso!
If you describe yourself as unaccomplished, you probably mean you haven't achieved your goals in a certain area. Being an unaccomplished poet can be pretty frustrating, especially if you dream of being the next Emily Dickinson. Someone who's more generally unaccomplished might just be a little awkward or clumsy. Both meanings come from the word's original sense, "not finished, or incomplete," and its Latin root, acomplir, "to fulfill or complete."