The title of this poem is crucial because it lets us know that the poem is spoken by Shakespeare's wife, Anne Hathaway. The epigraph, then, is a little piece of history: it's from Shakespeare's will, and tells us that the only item that he left for his wife in his will was their "second best bed." Score.
Anne Hathaway begins the poem by describing that second best bed mentioned the epigraph. She imagines that the bed is a "spinning world," filled with fanciful and beautiful things, like castles and clifftops. She describes Shakespeare's words as shooting stars, and then compares her and her husband's bodies to a whole bunch of poetic words like rhymes and echoes. And just to make it a little weirder, she tells us that she sometimes dreamed that he had written her, the same way he had written his plays. They had real romance and drama, though.
Finally, to clear things up, Anne says that their guests slept in their best bed, while she and her husband used second best one. (How generous.) Now, her husband lives on in her memory: she holds him in her mind, the same way he held her on their second best bed. Aw.