When you are dreaming, you take everything that happens for granted. It seems that your critical, rational side is absent. The strangest things happen, and yet it is absolutely normal.
In a lucid dream you don't take that anymore. You are conscious of your environment, and of the fact that everything that happens is not real. In other words: you dream consciously.
The Dutch poet and writer Frederik van Eeden was besides writing, also engaged with his dreams. He was the first to use the term lucid dreaming.
So the only difference between a normal dream and a lucid dream is that in a lucid dream you are aware that everything around you is created by your own mind.
Having a lucid dream doesn't mean you can control everything you want, or have some kind of double life in the dreamworld.
There are several gradations of consciousness in a lucid dream:
You have a nagging feeling that something is not right, but you can't put your finger on it. When you wake up, you realise:"Of course something wasn't right, I was dreaming! How couldn't I see?"
Low level lucidity
For a brief period you are conscious of the fact that you are dreaming, but you can't hold on to that thought. You get to interact consciously with your dream but without realizing you soon go with the flow of the dream again.
You are conscious of the fact that everything that happens is a dream and, that there is no real danger, and your body is safely asleep in bed.
Everything is very bright and clear. Colors are more intense, scents smell better, and it seems you can look infinitely far.
High lucidity will give you an enormous kick.
From the moment you fall asleep you know you are dreaming and you have everything under control. Rather than becoming conscious while dreaming, you go into the dreamstate consciously.