The title sets us at Kew, with a dog that belongs to royalty, and the poem opens on a scene of mock grandeur: silver plates that serve only sand. Something that looks rich turns out to be empty. A gentleman then explains "the meaning of dog" to the speaker, which sounds absurdly solemn. A dog is hardly a thing that needs defining, so the line pokes gentle fun at the man's self-importance and at the idea that polite society has a official answer for everything.
The second stanza shifts outdoors and into the dark. Walls, which are meant to keep things in or out, "secure the night," yet they also "call every fox / to take the air." The wild animals seem invited, as if the barriers make room for them. The speaker never says how they feel, but the tone is dry and amused, a little skeptical of formality. The mood is quiet and slightly surreal, and it leaves the reader leaning toward the foxes rather than the gentleman.