The speaker is an aging dog, or someone speaking through that image, looking back on a life of service and finding a quiet contentment in having finally settled. Where he once begged and waited on his master, he now rests. The word "pleased" sets the tone: there is no bitterness here, just a relaxed satisfaction.
The second half turns playful. The speaker's wife is "a fox," a sly, quick creature, while he calls himself "a dog of great families," a phrase that sounds like a pedigree, grand and a little self-mocking. Then comes the odd, memorable line: "I knew myself in Latin— / the best way to bow." Latin suggests formal learning, or the official names given to species and breeds. Knowing himself that way seems to mean being labeled and classified, and the poem treats it as a graceful form of humility. The mood is wry, calm, and gently humorous, with a thread of old-age acceptance beneath it.