Here is the biggest clue http://m.imgur.com/pUzAWbH

The entire movie is an adaptation of Carl Jung’s dream theory. Jung believed that our psychological maturity is achieved through our dreams, where certain “characters”, known as archetypes, take various forms to help us to merge our conscious with our unconscious selves. The theory is that every human is born with dream archetypes that fall into specific categories, though their exact roles vary from person to person. Common symbolic dreams are scattered throughout the movie as clues. The window breaking, Amelia eating glass, washing the bowl and then breaking it, the growling dog, bathing with clothes on, being unable to run away from a dark shadow, even the children’s book….these are all very common dreams with symbolic meaning. Samuel’s primary role in the movie is the Animus archetype, and serves as Amelia’s mediator between her conscious and subconscious, helping her integrate with her shadow. As the animus, Sam undergoes his own transformation throughout the course of the movie. The book itself is our first and biggest clue, as Carl Jung’s teachings (one’s shadow can be triggered by something someone says, or even the way they look—“It’s in a word or it’s in a look, you can’t get rid of the Babadook”) and even the Jungian symbol for SELF appears as the Babadook’s eye on the page that reads “If you’re a very clever one, and you know what it is to see, You can make friends with a special one, a friend to you and me.” Imgur link attached. Every detail of the movie is significant in some way, and each character is portraying a classic archetype (the divine child, the mother, the old woman, the wise man, the shadow, the animus, the trickster, etc.). Play close attention to the colors used throughout the movie as well. Jung was a pioneer of color psychology, and the use of black, white, yellow, pink, and burgundy/red (specifically in the characters' clothing) tells it's own story. In the final scene, After Amelia integrates with her Shadow (the Babadook), we see Samuel take on the trickster archetype (as an incredibly skilled magician), and hitting the bullseye while playing darts (a classic dream symbol for hostility). These are signs that Amelia is misguided in her belief that all is well, because now the Trickster has become the neglected archetype, and has gained significant power by her ignoring his existence. The black rose seen in the garden is a common symbol for fantasy—the opposite of reality. Samuel reinforces this when he says “Things are not as they seem.” Jung famously said “Show me a sane man, and I will cure him for you.” Basically, that wholeness, or mental health, is a never ending process. You will always be a work in progress, because different parts of your psyche will need attention at different times.

I can post more later elaborating on the topic and getting into all of the specifics of how Jung's Integration relates to the movie. Overall, I seriously could not be more impressed with this movie. The harder you look the more you see.