Typical characteristics of Confessional poetry are :
-The use of "I" stories
-Descriptions of personal life (including family trials and personal struggles)
-Craft was true to poetic conventions and forms
The most famously known Confessionalists were Anne Sexton, Robert Lowell, and Sylvia Plath.
Given that the poetry of Sylvia Plath dealt with themes common to typical works of the Confessionalits (suicide, death, and mental illness), Plath definitely fits properly into the category of the Confessionalist.
Her poem "Barren Woman" deals with her inner feelings about her depression. In the poem "Daddy", Plath openly talks about murdering her father (perhaps figuratively based upon personal interpretation "Daddy, I have had to kill you"). The poem "Cut" includes Plath's feelings on injuring herself superficially to ending her life- "I have taken a pill to kill."
Simplistically, any work in which one openly discusses and states personal feelings regarding their own life and the happenings in their life would be considered Confessional.