Answer:
He said that he's "a traveler in want of a little rest" but in reality, he was hoping for more than that. He wanted to be alone with the old man, with enough time to make the old, blind man, like him. And in that chain of events, the younger occupants may also come to like him eventually. And then he'd finally have companionship and not be lonely anymore.
Step-by-step explanation:
Mary Shelley's "Frankenstein" revolves around a young scientist, Victor Frankenstein, and his desire to gain knowledge beyond human capacity. And in that desire, he created a monster, making him parallel to the gods by giving life to a new being.
The creature had been abandoned by his creator. And in his desire to have companionship, he was traveling the world to get to Victor. On one occasion, he came upon a family living in the woods. He stayed hidden, with a plan to introduce himself and hopefully, be accepted by them and become a part of their lives.
The given line said by the Creature is an example of verbal irony because what he said and what he had actually planned or wanted was different. He wanted to introduce himself to the blind, old man, and hope that his acceptance will encourage the younger ones to accept him too. Despite his horrible appearance, since the old man is blind, the Creature hoped he doesn't judge his voice; "My voice, although harsh, had nothing terrible in it". But what he actually wanted was to be able to have enough time to get the old man to know him, accept him and welcome him to their family. And this, in turn, will hopefully make the younger occupants obey the old man and accept the creature too.
So, when he said he's a traveler and wanted a little rest, he was rather looking for a chance to prove his goodness and maybe possibly get accepted and be a part of their family.