Everybody dreams. Some dreams are the stuff of legend (or vice versa.) Everyone has to dream. It's your brain attempting to organize the events of the day and say high to your subconscious. In some settings dreams may be prophetic. They may be the medium for spirits to mortal men. By their very nature they have a certain ambiguity. Was it your deceased business partner speaking to you from beyond the grave or a fragment of underdone potato you had for dinner?
Dreams are ideal for providing nudges to player characters while leaving some ambiguity to the world. Are the gods who speak in dreams real? Some dreams do change the world: Mary Shelley got the idea for Frankenstein from a dream. James Cameron was inspired to write Terminator by a dream. Elias Howe figured out how to construct the sewing machine from his dream and Frederick August Kekule discovered the chemical structure of benzene when he had a dream of a group of snakes swallowing their tails.
So dreams could be a way for the GM to introduce new and novel discoveries. Maybe bizarre steampunk inventions are designed in a dream state and constructed when the inventor awakes, without their control. Likewise spells for a spell book could come to you in dreams. Maybe you got those six detect spells in a row for a reason, when you were itching for fireball?
The ambiguity of dreams also works for certain beings. Cthulhu and the Great Old Ones communicate to humans through their dreams, but no one is going to take a loony babbling about a vast, shambling horror seriously. If you need a warning for a dire threat but don't want anything the forensic boys can analyze for Cthulhoid slime a dream is the way to go. Perhaps there is a sinister purpose behind that dream you had of an immense and wonderful mechanical marvel.?
Besides sending dreams some beings might be able to attack dreamers through them. A dreamer might defend himself using his skills and attributes normally or might have a cliche or skill to represent 'Dream Savvy' for foghting or shaping his dream world. Several movies have dealt with combat and adventures in the Dream World.
Is there a Dream World? A GM has to ask himself that. Do people's spirits go into this world? Can they be transported there physically? Do creatures and places encountered in a dream have an existence separate from the dreamer? Finally, can you go from one dream to another?
Dream related powers or spells are extraordinarily powerful. No matter how powerful or well guarded a person is, they must sleep sometime. You may be able to move mountains in the waking world or lead armies but we are all equal and equally vulnerable when we sleep.