The Dreamworld can be two different things.
The Dreamworld realm is a dimension where most Dream dragons live. It can only be accessed by humans using magic. Dragons can come from this dimension into someone's morpheon. We created a way you can look at the Dreamworld without actually entering it, as if you enter it strange things may happen, which can make you insane or worse, die.
A Morpheon is somebody's dreamworld and the location where their dreams happen. It is part of the larger dreamworld that the Dream dragons inhabit in a sense, except that it is bound to your mind and memories, so you cannot venture deep into the Dreamworld where only dream dragons exist during natural sleep. It was long thought to be just part of your imaginary, though it is demonstrated that it is, in fact, accessible and dragons like the Nightmare Dragon can enter your dreamworld and devour everything pleasant and happy to feed itself. The dragon cannot be seen in your dreams, but its presence will change your dreamworld, producing nightmares. This effect is balanced by the Dream Dragon, which eats nightmares, displacing them with pleasanter dreams. Both are necessary to provide balance in the dreamworld. Nightmares are often caused by an unbalanced morpheon--even a proliferation of positive dreams can lead to an imbalance, causing the dreamworld to shift in the opposite direction and producing nightmares.
Other Dream dragons can access your morpheon and reside there too, but they will go away before you wake up. However, if you work strong magic while you sleep or wake up spontaneously but without help the dragons will be pushed out of your morpheon into the "real" world or whatever dimension you are in at that moment. Dream dragons can also choose to exit the dreamworld, but this is rare.