The speaker of the poem is a child, who finds a picture of her father, and tries to understand him. (We’re not told if this speaker is a girl or a boy, but for the purposes of this answer, I’ll read her as a girl).
Its message is that even people who are behaving badly, have histories, hopes, dreams and good aspects to them.
The poem is divided into three stanzas. In the first stanza, the girl tells us that she’s found the picture, but she mostly speaks about her father’s more recent behavior. Pabst Blue Ribbon is a beer and the poem tells us about the father’s abusive behavior, when he is drunk.
In the second and third stanzas, the narrator looks back to the earlier, happier times depicted in the picture. Then, her father had hopes and dreams, and she could feel that he loved her. This time is what gives the poem its title, Heaven.
The poem repeats words, ‘before,’ and ‘he’s’ to remind us of the difference between the two times. Importantly, the conceit of the picture allows her to speak about those earlier, happier times in the present. The poem’s simple diction allows us to sympathize with the child. The poem’s rhythm keeps us moving forward in the poem, even though the poem moves from the present to the past.
The speaker in the poem is an adult, looking back, through the conceit of the photograph, at a simpler time before (her) family fell apart, and in particular, before the relationship with her father deteriorated. Details of the photo can be taken both literally -- "it's in black and white" -- and figuratively -- life was simple, not questioned. The speaker further says that the photo, which was taken in 1963, hence the title, Heaven, 1963, is her favorite because she can see her father before life overwhelmed him and took away his "dreamy expression."
The poem is, at its core, a poem that explores the pain of loss, including the loss of innocence. It's also a love poem to the father by way of an acknowledgement that before life's turns -- alcohol, marital difficulties, rage -- that took away the father's innocence -- "he's wearing sunglasses, a light cotton shirt," -- the father found joy in the simple pleasure of holding his 2 year old daughter.
The poem also explores the child's (now adult) loss of her innocent world view, her "baby curls" and the absolute peace and safety of "being fast asleep" in her "father's arms."