We don't know all that much about the speaker of the poem. We don't even know his/her gender! (We are going to refer to the speaker as a woman, though, for the sake of simplicity.) We do know that she has an Aunt Jennifer and an Uncle. We also might guess that the speaker is a child, because of the intimate way that she refers to "Aunt Jennifer" (and not, for example, "my Aunt Jennifer"). It's as if Aunt J is already the speaker's confidante, or at least close relative.
Beyond that, there's not a lot of setup or explaining in this poem. The speaker just jumps right in and expects us to follow along. The poem is also written in couplets (rhyming pairs of lines), and thus the poem feels a bit sing-songy. These two things make us feel like we're listening to a young speaker. This is significant because, as child, the speaker would be looking up to her married aunt as an example, a role model. In that way, the poem suggest that Aunt Jennifer's struggles might set the stage for the future struggles of the speaker. And that would be totes sad.
Or, we can turn that frown upside down (we can't believe we just typed that) and say that Aunt J's triumph through her craft (those thrilling tigers) sets an example for the speaker about how to overcome repression and find your true voice through art. If we substitute Adrienne Rich for the speaker, then, (though it is always dangerous to presume that the speaker is the poet), we could say that Aunt J made a great role model for the speaker—this poem is perfect proof!