Anne Hathaway was Shakespeare's wife. Although we don't know too much about her, we do know what Shakespeare left for her in his will: their second best bed. While a lot of Shakespeare scholars assume that this was a sign that Shakespeare didn't love her, Duffy interprets the will differently in the poem. The second best bed in "Anne Hathaway" is a symbol of love and devotion.
We may never get to know the real Anne Hathaway, but we get to know a fictionalized version of her through Duffy's work. She's a talented writer herself, and she appropriates (or borrows) a lot of Shakespearean stuff for her own sonnet. She's also a very sensuous woman, and recounts her passionate experiences with her husband in great detail. And like Shakespeare, Anne loves metaphors. (Can you tell?) For example, she describes her husband's words as kisses that fall to earth like shooting stars. Now that's poetry!
Anne is not at all angry about Shakespeare's will, but she certainly does want others to understand their relationship. This poem is a rebuttal to all those people who think that Shakespeare didn't love his wife, and it's straight from the horse's mouth. Duffy's Anne is basically saying to them: he loved me, I loved him, we had awesome sex, and I'll always cherish our second best bed. So mind your own business and don't go nosing around in other people's wills.