Why is it so hard to remember what we have dreamed about after we wake up?
Although we don't have a firm answer to this one, it obviously has to do with how memories are formed, and the fact that they are formed differently when you're dreaming than when you're awake. There are, unfortunately, a couple of different theories. One says that because of the altered chemical environment in the brain during REM sleep, the brain is literally unable to form new memories. The only way to remember a dream is to wake up out of the dream while it's still fresh in your mind, and then rehearse it in the wake state. According to this theory, it's during the process of rehearsal that the actual memory is formed so that you can remember it later.
The second theory says that memory formation is fine during REM sleep, but that recall is very difficult. This theory is strongly supported by those times when something happens during the day, like a dog runs out in front of a car and almost gets hit, and you suddenly say, "Oh wow, I had a dream last night with a dog running around in it." The argument here is that the memory of the dream is there in your memory (when you recall the dog dream, you see the whole dream segment with clear visual imagery, recalling your feelings, what else was going on, etc.) but until the dog appeared the next day you had no associations that would allow you to locate and recall the memory of the dream. After all, if I try to remember where I left my car keys last night, I have a strategy for searching my memory - what did I do after dinner, where did I go, when did I come home, what did I do when I came back into the house, etc. But if I want to recall my dreams from last night, where do I look for that memory? Unless we can hold onto the images in our mind when we first wake up, and then use then as a pathway to the memory of the rest of the dream, we seem to be out of luck.
Another curious quality of brain activity during dreaming is that almost all dreams are forgotten. Dream amnesia is the norm. This is not due to anything paranormal or supernatural, but to weak encoding. Memory depends upon encoding the data of experience. Encoding depends upon connections in parts of the brain, which in turn depend upon connections in experience. An event with a strong emotional component is more likely to be remembered than one with no emotional component because emotional memories are recorded in one part of the brain while visual components are recorded in another. Neural connections link them. We are likely to remember dreams if we wake shortly after they occur. Even so, if we do not encode the dream by making some effort to remember it, we are likely to forget it. Some people assist memory by getting up and writing down the dream. Others find that an easier method is to stay in bed and create some associations. The easiest association is made by giving the dream a title and a purposive description. For example, a dream of being chased by a polar bear across the snow into a library might be labeled "Research the Polar Bear." Go back to sleep and you are likely to remember the dream by recalling the title.
Introspection suggests that dreaming is a conscious activity, and that idea is supported by the waking-type EEG patterns that typically accompany REM sleep. Yet perhaps all of us have experienced awakening from a dream and only remembering its very last portion,if any of it at all. This phenomenon is referred to as dream amnesia. Neuroscientist Paul Adams theorizes that both slow wave sleep and REM sleep are required for the offline updating of thalamocortical circuits during learning (consolidation of DM, aka 'Declarative Memory') (Cox &Adams 2000). Updating one of the circuits requires activity provided by the random auto-associations of dreaming, while the other needs the relative quiet of deep sleep. Thus the imaginary contents of dreams would play no useful role in DM; they are not to be learned. The IDA model suggests that during sleep, just as motor activity is suppressed, so also is the function detailed in Step 5 whereby conscious contents are stored in TEM (AKA: 'Transient Episodic Memory'). Hobson and Stickgold have suggested a neural mechanism for this phenomenon in terms of cholinergic activity during REM sleep (1994). Thus the only memory available for the recall of a dream is the small capacity WM (AKA: 'Working Memory'), resulting in dream amnesia. The limited capacity of WM would yield a memory only of the final small portion of the dream. The rapid decay of WM would account for no memory of the dream at all after a slow awakening.
(http://www.cs.memphis.edu/~wrcm/MemorySubmit.pdf for the full document above)