Tannin is a bittering agent. It's to red wine what hops are to beer. Hmm, I might get flamed for that... The bitter flavor helps balance the flavor of the alcohol. Tannin generally starts very sharply bitter. Over time, and in the presence of alcohol, it changes to a more mellow pleasant bitter flavor. The caffeine in the tea also helps the yeast out. Since mead tends to ferment slowly, that's a nice side effect.
Powdered tannin is more controllable. Coffee has more caffeine, and nitrogen. Coffee has a flavor that is generally considered undesirable in mead though. Powdered caffeine is harder to find, and slightly dangerous to handle. Tea is cheap, readily available, and usually comes in a handy bag for extraction.
Everyone brews a bit differently. There is nothing wrong with adding tannin powder, tea, or no bittering agent, to mead.