In a nutshell, a false awakening is where you feel as if you are waking up and you dream of doing daily morning activities. It normally comes in 2 types;
Type 1: This one is more common. Usually you wake up in an environment that is completely off reality. In some cases you wake up not in your bedroom.
Type 2: This one is quite rare. This one is harder to pick out weather it is a dream or reality. Usually you wake up like you normally would, and it would seem very much like reality. It is only later you find things are slightly incorrect from what normally happens.
More information:
http://en.wikipedia.org/wiki/False_awakening
I've had type 1 about 4 times and I'm quite lucky as I've had type 2 around once or twice.
Discuss times when you've had false awakenings(If you remember it.)