One is lucid dreaming when one is aware that they are dreaming during the dream.  This is the most basic of definitions.

Many people that lucid dream will also play around with the dream and do things they would not normally do during awake hours.  They may fly, walk though fire, or engage in activities that they normally would refrain from.  In addition, they may change events or characteristics of the dream much like in the movie, Inception.  While all this may occur in a lucid dream, the only attribute necessary to make the dream “lucid” is the fact that the dreamer is aware they are dreaming.

Lucid dreaming should not be confused with people that astral project during their sleep.  Such people actually leave their body and travel about during their sleep.  I have known several people that astral project during sleep (which can be a problem when your ex-boyfriend does too) and what they describe does not sound like a dream state.  I have also read that people can share dreams, but I don’t know anyone that has ever talked about this.  I’m curious how it is different from an astral projection meet-up – or if the difference is just in the person’s perspective and the words used to describe it.