Amplification is a little like the process of association mentioned earlier. Amplification is looking at the images that you create and are surrounded by, amplifying them to their furthest range of archetypes and associating them with parallels from other areas of the humanities (religion, literature, etc.). It can be described as a form of creative imagination or guided imagination (guided by awareness of archetypes and shadow).
Amplification is a necessary process for individuation because when we are in the throes of a certain archetype or shadow or anima/animus image, we don’t know it (otherwise, we wouldn’t be at its mercy). 
But by amplifying the images in our dreams and imagination and words, we can “figure out” what is going on psychically in our lives.
Amplification can help make sense of something that seems important to the self in its everyday life by showing how it relates to more universal patterns and stories (archetypes). Thus, it can help you see likely outcomes and possible courses of action. 
Once we see what is going on with us psychically, we can react accordingly. We do not always want to dismiss or counteract what has a hold of us. Some archetypes help us get through life’s difficulties by providing a model for how we should behave. Some elements of the shadow can be sources of great creativity and energy. But we do need to be aware of them so we are not “hijacked” by them.
An example of using amplification off the top of my head:
You’re talking to a friend and you say, “This morning I woke up and turned off my alarm rabbit.” You might look at what you associate with the rabbit. What gods are personified as rabbits. What attributes do rabbits have? What are other words for rabbit? What are other images like rabbits? What are famous rabbit images?
There is a famous trompe l’oeil trick of the eye drawing depending on how you look at it it’s either a rabbit ears or a ducks beak. 
So maybe the Jungian slip of rabbit is meant to take you to duck. Maybe it is meant to show you that time, like the rabbit duck image, can change depending on how you look at it. Or maybe it was just your subconscious warning you not to be late, 
like the rabbit in Alice in Wonderland. Are you worried about being late to a specific appointment that week? Or late to doing something to save your marriage? Or late to writing that Great American Novel you were always planning to write? 
By starting with a seemingly trivial image from your daily life, amplification can help you learn what the psyche/soul is really worried about.