Of course there are primarily unconscious areas of the brain, such as the amygdala, seat of emotion, and the cerebral cortex, seat of consciousness, and clearly they they communicate with each other. When you are in love, for instance, both areas are active, one conscious, one unconscious.
The reality of the unconscious (better term than subconscious, but often used interchangeably) can be demonstrated in several ways. Here are 2:
1. When you are sleeping, you are unconscious. Therefore any brain activity, such as dreaming, is unconscious. You can never recreate exactly this unconscious activity, but may recall parts of it. The parts you recall demonstrate the connection between the unconscious and the conscious.
This is why Freud called dreams the royal road to the unconscious.
2. Try to remember the very first time you saw your wife, or husband, or girlfriend, or boyfriend, or someone very significant you met as an adult. This memory is conscious. Now try to remember the very first time you saw your mother (assuming you were an infant). Where is that memory? Have you forgotten it? Now remember the first 700 times you saw your mother, every single day for the first 2 years of your life. Where are these memories? Completely forgotten? No, they are there, but unconscious. They are all in there somewhere, influencing you even as you read this. Hopefully, she treated you well and you're emotionally healthy. But if she mistreated you, you'll bear the scars forever, manifested by bad behavior, bad mood, and (probably) bad dreams. You'll go to the shrink with your problems, and you'll both be befuddled by the root of it all. And Mom, bless her heart, will never admit that she messed you up.