When authors capitalize a word or name, they usually do it to emphasize the importance of that word. They want to make it stand out from the others, or attach some sort of significance to the title.
In "The Listeners," Traveller is probably capitalized for a couple different reasons, all of them pointing to a greater emphasis on the importance of this man in the story's telling. First of all, he is the only "real" character in the tale; the only other presence in the story is that of his horse, and of the "host of phantom listeners" that receive his knock in silence. Because he is the only tangible character, the author might have capitalized the T in order to emphasize that he is the one and only person in the poem.
A more likely reason is to emphasize how important the Traveller was to the listeners within the house. From reading the poem, one can infer that he has come a very long way, and has been very anxious about delivering his message. He also has a very important message to deliver, because he does it so anxiously, and to a house that is most likely empty of living occupants. There is hinted at some secret, vital mission, and that delivering his message is something that these "phantom listeners" have been waiting for for a long time. That makes this man, and his message and visit, very important. Hence, he is the Traveller, the one they've been waiting for, the man with the message. Not just any traveller on the road, stopping by the house, but the Traveller that is fulfilling whatever mission has been given to him. The author emphasizes his importance, and the importance of his message, through that capital T.
I hope that those thoughts helped; good luck!