"Anne Hathaway" is a poem about writing as much as it is a poem about love. Duffy compares sex to writing throughout the poem; sometimes it's even hard to figure out which she's talking about. Shakespeare is considered by many people to be the greatest writer ever, but in this poem, it's his wife Anne who's got the skills.
This poem suggests that Anne Hathaway subordinates her writing powers to her husband's (meaning that his are more valuable). The poem is just a tribute to her husband's skilled writing.
This poem shows that Anne Hathaway is just as talented as her husband was. She just never got to show her skills because of the time and culture in which she lived.