Image is the root word, so imaginary is an image only in the mind, not real.
Some people recount having had an imaginary friend as a child. I never did. However, I did use my imagination in other ways. I had, for a short time, an imaginary place, a jungle. It was simply (on our large block) my father’s overgrown veggie patch where I hunted tigers and lions and camped. I also remember lying on the grass, looking up and seeing all sorts of things in clouds (I still do).
‘Pan’s Labyrinth’ is a profound movie. Though dark and confronting, it shows how we use imagination, how the imaginary works, how it can be an insight into our self.
Both Freud and Jung worked positively with the imagination, as with dreams, it is a key or gateway to the inner workings of a person. the imaginary always lilnks to something real, something experienced, something known.
The imaginary fires creativity too, design, art, film making, writing, engineering, play, all use imagination.
In that sense, imaginary may be, on the surface or to the untrained person, not real. But to the insighful and the aware, the imaginary is an insight to the workings of the self and a portal to creativity for all ages.