Dreams during which the dreamer is conscious and aware that he is she is dreaming while the dream is taking place. Lucid dreamers can often manipulate and otherwise participate actively in their dreams. The sensation is as if you wake up and are still in dreamland. The remarkable thing about this dream state is though you feel very awake, the sleep quality you receive is still very deep and leaves you feeling refreshed.
The term lucid dreaming was originally created in 1913 by Frederik van Eeden (a Dutch psychiatrist), but it was Keith Hearne who proved that they exist. He did this by devising an experiment where the dreamer would let him know that they were lucid dreaming by using a pattern that was decided before the person went to sleep. In the case of this experiment the proof came in the form of eight side to side eye movements.
Many people find lucid dreams to be fun and want to induce them. Common things that have induced that type of dreaming for some people along with extensive history can be found here: http://www.susanblackmore.co.uk/Articles/si91ld.html
Example: A man is having a frightening dream about being chased but knows he’s asleep. Since things are able to be manipulated in a lucid dream and anthing is possible, he decides to fly away from his pursuers, steering the dream toward happier content.