A dream in which you believe you have woken up is called a "False Awakening". 

 

False awakenings are common among those learning to lucid dream and are a good reason to remember to perform a reality test whenever you think you've woken up.

 

Dreams are often built upon expectations, so because we expect to wake up, often we'll dream about doing so. This is especially true when a lucid dream fades and you believe you are about to wake up.

Remember, perform a reality test whenever you wake up during the night!