This poem is all about laying emotions on the line – even if those emotions aren't exactly the sorts of feelings that most "polite" society would want to acknowledge. You might even say that Plath allows her speaker to confess her emotions to the page (and, by extension, to us as readers). She addresses feelings directly, sorting through all of the complications of love and motherhood and personal identity that get bundled into the speaker's experience of her child's birth.
Confessional poetry may be Plath's calling card, but it became the form of plenty of other mid-20th century poets, as well. In fact, they named an entire movement after it. Check out what the American Academy of Poetry has to say about confessional poets here.