In just two short couplets, the speaker compares a haircut to confession. Sitting under the barber's hands, he feels the kind of release people usually look for in a confessional: a place to put down whatever the day has piled on him.
The comparison works because of how the two settings overlap. In both, you sit still, you hand yourself over to someone else, and you let go of a little control. The "dancing combs" give the scene a light, quick motion, as if the barber's work is almost a gentle ritual. Nothing heavy is said about what the day contained, and the poem doesn't tell us. What matters is the relief of setting it down.
The mood is calm, quiet, and a bit tender. The phrase "I would go" suggests this is a habit or a wish, not a single visit. The poem seems to find something close to sacred in an ordinary, everyday service.