I'll give you two examples of a false awakening that I had:

1) I needed to go to the bathroom in the middle of the night, but instead of actually waking up, I had a dream that I got up, went to the bathroom, turned on the light, urinated, and crawled back into bed. Then my body realized it still needed to go to the bathroom. So I *actually* woke up.

2) I usually immediately write my dreams in my dream journal notebook which is right to the side of my bed after I wake up. I have *several* false awakenings in which I think I am awake, writing my dreams in my dream journal, but in reality, I am still asleep. All I remember is the fact that I am writing my dream down in my dream journal, but I can't remember the dream I was trying to record!