Definitions for "False Awakening"
A vivid or lucid dream experience in which the subject believes that he or she has awoken from sleep, but is in reality still very deep in dreaming.
A false awakening occurs in a dream when you think you have just woken up from a dream, but really you have not.  An example of a false awakening would be that in a dream you find a bag of money, then you wake up and find the bag of money beside your bed, and then you really wake up to find that the money bag is gone.  This can happen more than one time within a dream and tends to make you quite confused.
A phenomenon whereby a person believes they have woken up but they are still dreaming.