The speaker pictures themselves as a wolf surrounded by dogs, in a place where everyone is snarling. Instead of snarling back, the wolf howls "long and pretty," which suggests a choice to be beautiful, or at least sincere, in the middle of hostility. Then comes a retreat: down a hole until dark. The speaker doesn't fight and doesn't quite belong, so they hide and wait.
The last two lines widen the idea. The world runs by a clock that is "full forward," pushing ahead at speed, while the speaker's own day is "quiet and backward." "Backward" could mean old-fashioned, slow, or turned inward, and the poem leaves that open. The mood is calm but a little lonely. There is some pride in being different, and some weariness too. The speaker seems to prefer solitude and quiet over the noise of the crowd, even if it means being out of step.