It's an interesting phenomenon called 'False Awakening' or FA for short
There should be a lot of previous topics on it, if you do a search
They can be used as dream signs - that can be used to become lucid

It can get pretty freaky too - waking up from a dream and then waking up into yet another dream... and then only really waking up
In fact, there was a guy on dreamlucidity.com (I think), who was an experienced LDer
He went to sleep, dreamt of some people at his place (not lucid at all)... he went upstairs, and did a WILD
He had a fully lucid dream, then woke up into the *previous* dream about his house and the people.
He finished the normal dream, as usual, and then woke up to realise what just happened!

Quite amazing thing really, the way dreams can be 'nested' inside each other...