When you do something afresh, you start it again as if it's the first time. You might, for example, start afresh baking a new apple pie after burning the first one.
When you see the adverb afresh, it's often following "start" or "begin." Doing something afresh is getting a fresh start, or a complete do-over. Your grandfather might start afresh with his new job as a goat farmer after a lifetime working as an accountant. Or you might start afresh with a classmate you used to argue with, determined to find a way to get along. In both examples, someone is approaching things in a brand new way.