Recap: Tiresias prophesizes that Narcissus will live to old age, "as long as he never knows himself." And… that's it.
While Tiresias just plays a bit part in the Echo and Narcissus story, he is a pretty famous character in ancient Greek mythology as a whole. As a prophet of Apollo, he is gifted with glimpses of the future, both through visions and by listening to the speech of birds. Fancy.
Oh, also, he's blind (not uncommon for mythological and literary figures who can see the future). Some versions of his story say that he was struck blind when he accidently spotted Athena bathing naked. Others say that Hera blinded him for taking Zeus' side in an argument about who enjoys sex more, men or women. Well, then.
Regardless, Tiresias appears consistently in myths about the city of Thebes and its history. Some of his most notable appearances include Sophocles' Oedipus Rex and a rocking appearance from beyond the grave in Homer's Odyssey.