The speaker does something odd with a very ordinary errand. Instead of asking the barber for a haircut, he tells his mind to the barber, as if the head and the thoughts inside it were one thing to be trimmed and tidied. The request is to "put things in order," and the last line, "to go away," is nicely ambiguous. It could mean the barber should make the mess leave, or that the speaker himself wants to leave, to get away from his own head for a while.
What comes through is a quiet weariness. The speaker seems cluttered and a little overwhelmed, and he wants someone else to fix it, as simply as getting a haircut. There's gentle humor in that idea, but also something wistful, since we all know a barber can't really do this. The mood is light on the surface and slightly sad underneath, a small wish for calm told in just a few plain words.