A lucid dream is one in which you're aware of the fact that you're dreaming and can often control what happens. It's a powerful skill to develop with many delightful applications: dream debauchery, amplifying creativity, practicing athletic skills, managing psychological stressors, etc. Recently though, sleep scientists have renewed their interest in lucid dreaming as a way to possibly gain insight into the mysteries of human consciousness. For example, in one study, an experienced lucid dreamer managed to snooze while undergoing an fMRI scan so that scientists could watch which parts of his brain lit up at particular times. From The Guardian:
[Most sleep researchers] would agree that lucid dreams involve an increased self-awareness and reflection, a greater sense of agency and volition, and an ability to think about the more distant past and future. These together mark a substantially different mental experience from the typically passive state of non-lucid dreams.
"There's a grouping of higher-level features, which seem to be very closely associated with what we think of as human consciousness, which come back in that shift from a non-lucid to a lucid dream," says Dr Benjamin Baird, a research scientist at the Center for Sleep and Consciousness at the University of Wisconsin-Madison. "And there's something to be learned in looking at that contrast." […]
[In other scientists' 2012 study,] brain scans revealed heightened activity in a group of regions, including the anterior prefrontal cortex, that are together known as the frontoparietal network. These areas are markedly less active during normal REM sleep, but they became much busier whenever the participant entered his lucid dream – suggesting that they are somehow involved in the heightened reflection and self-awareness that characterise the state.