A lucid dream is being aware of yourself dreaming. This allows you to participate in the dream, and do unordianry things to your own commands.
Lucid dreams help to also ease nightmares. Being aware that your just dreaming helps you come over the fact that the nightmares are of no threat.
So, overall summary;
You're asleep, but are aware that you're sleeping. Normally dreams are uncontrolled by you and sometimes (in the case of nightmares) pose a threat, as you assume this to be happening really. Lucid dreams aware you that you're dreaming, so you could make yourself fly, teleport, etc. Okay?
If you are interested in this, there are many ways to cause lucid dreams. Otherwise they'd rarely happen naturely;
Note all your dreams for the previous night.
Noticing a pattern in your dream allows you to recognise the properties of your dreams. When you sleep nights later, you'll be able to recognise the pattern of the dreams occuring again, allowing you to aware yourself that you are dreaming.
If there's any confusion, wall me.