This is a poem talking about the issue of a woman's life. But I don't think that Adrienne Rich really had an aunt by this name. Somehow, Aunt Jennifer is just a representative of the married women. In the first stanza, the speaker tries to give us an image of how her Aunt Jennifer's work looks like. There are tigers prancing across the green screen. And they are afraid of nothing in their world including the men beneath the tree; as the speaker says they pace in sleek chivalric certainty.
In the second stanza, the speaker starts to describe her Aunt Jennifer. I think that most women would agree that after getting married the time and the freedom are somehow limited by their husbands, children or even their own ideas about being a wife and a mother. But in the second stanza, we can easily find out how the speaker emphasizes the marriage would make a woman oppressed. She says "The massive weight of Uncle's wedding band sits heavily on Aunt Jennifer's hand." I think it's not hard to have an associate idea that the wedding ring here means the marriage or the husband. So we can see how the speaker put emphasis upon the limit of the marriage to a woman. As we all know how a wedding ring could weigh, it must weigh not over hundreds of grams at large no matter how many diamonds it could possibly have. So, how could a light wedding ring be so heavy that even make Aunt Jennifer's hand feel hard to pull the ivory needle. It is not the wedding ring that make Aunt Jennifer's hand weak but its most equally representative thing-marriage- that drives Aunt Jennifer's hand weak.
In the third stanza, the speaker again put emphasis how marriage would drive a woman's life till she was dead. Or we should say that even Aunt Jennifer was dead she was still under the oppression of marriage since the speaker says "When Aunt is dead, her terrified hands will lie still ringed with ordeals she was mastered by" When Aunt Jennifer was dead, the wedding ring might go with her, clinging to Aunt Jennifer's finger. I think that no matter Aunt Jennifer was dead or alive, the wedding would go with her just as the speaker says. Only the spirit of Aunt Jennifer would be set free like the tigers she wove would go on and keep prancing proud and unafraid.