The Treehouse is house that both Katerina Kittycat and O the Owl both live in along with their parents. Both characters are neighbors and live practically window to window with one another. It was first seen in the episode Daniel's Birthday when Trolley stopped by the treehouse with Daniel Tiger and his mother.
In "A Trip to the Crayon Factory," when Katerina exits the Trolley to go into the treehouse, she goes around the back of the tree, meaning that there is some sort of backdoor that the treehouse can also be accessed with.