Lucid Dream is a dream where a person knows that he/she is in a dream while the dream is in progress. (Some sort of a matrix like world where the rules of normal world can be either bend or broken. Just think of possibilities.)
Its one of the wonderful things when your unconscious mind interacts with your conscious mind.
What we see or perceive is a model of the world created by our brain based on the inputs received by our senses. During a dream similar model is picked up by the brain just the input is not added from sensory organs instead given by unconscious mind mostly the thoughts the person is going through. During Lucid state we can add some inputs from our conscious mind too.
Its far more difficult to have consistent lucid dreams than the first one but a great thing to explore.
Have Fun :)
Wikipedia
Lucidity