This when you dream of waking up. You will be fooled by it, and think you are really awake. If this happens to you frequently, then a good idea would be to reality check immediately when you wake up. This is a very reliable way to DILD (Dream Induced Lucid Dream) if one has frequent false awakenings.
A slightly different form of false awakening, sometimes referred to as an INRALD, may occur when trying to WILD. You may not be aware that you have transitioned from awake to sleeping, and you are actually dreaming of lying on the couch/bed or wherever you attempted your WILD from. Catching an INRALD is usually done by reality checking after experiencing any hypnogogic hallucinations or other transition-like effects (such as vibrations, or loud noises in your ears).
DILD - Dream Induced Lucid Dream
HH - Hypnogogic Hallucinations
WILD - Wake Induced Lucid Dream