Differential Manchester encoding is a line coding technique that encodes binary data by ensuring a transition at the middle of each bit period. It works by inserting a transition at the middle of each bit period for a 1 and no transition for a 0. Some applications of differential Manchester encoding include magnetic storage and optical storage. It has advantages like self-clocking and no DC component, but also has disadvantages like requiring transitions for both 0s and 1s, reducing bandwidth efficiency.