This is a really interesting question. Normally, when we capitalize a word in English, we are drawing particular importance to it—or else it is standing in for a proper noun, like a name. Sometimes we use a capitalization for someone's title to indicate that they are important or singular, even though we aren't using their name—such as God or Bishop. In this instance, "Traveller" is capitalized in such a way that it designates the Traveller as the protagonist of the poem, a particular and specific character. He is not just any traveler passing through the woods, but is the specific Traveller who has sworn to return to this house "the one man left awake." He is not one of many, but a man alone. However, the effect of calling him "the Traveller," rather than giving him a name, adds to the eerie mood of the poem, whose atmosphere depends upon mystery and suspense which is never resolved.

This is a good question. Of course, we can't go back in time and ask de la Mare why he capitalized it, but there are two possible explanations. 

The first reason is that "The Traveller" functions as a proper name. He is the protagonist of the poem and is given no other name, and so within the context of the poem, this is his name, and proper names are normally capitalized in English.

A second reason has to do with genre and intertextuality. The poem is echoing the tradition of early English literature in which characters were named by their characteristics. One finds this sort of naming convention in morality plays such as "Everyman" or Bunyan's Pilgrim's Progress (an early modern allegory that derives from the morality play tradition in certain ways). Thus the capitalization, in evoking the older tradition of characters named by their characteristics, suggests that we should not read this as a narrative about the personal experiences of "The Traveller" but rather as a reflection on the way all people relate to things in their past. 

In "The Listeners" by Walter de la Mare, why is the Traveller capitalized?

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!