Roughly, we spend 6 entire years of our lives dreaming. Although we can be "aware" of what happens in our dreams, we're clearly not conscious in the same way as when we are awake. link
But some people, in particular lucid dreamers, have the ability to experience awareness while they dream by "re-awakening" aspects of their waking life consciousness. Like Leo in Inception, they can even control and act with intentionality in their dream world.
According to a study done by Discover Magazine, about 50% of people will experience at least one lucid dream during their lives. There is also some evidence that lucid dreaming can be induced and does not need to be regulated to an accidental anomaly.
Incredible studies have examined the difference between lucid and non-lucid dream, and what goes on in the brain during this time, by hooking people up to a brain scanner over night and comparing brain activity. They have developed a communication between lucid dreamer participants and the researchers themselves. Before going to sleep, the participant and the research agree on a specific eye movement in order to signal that they are currently lucid dreaming.
This way of testing has shown that the difference between non-lucid and lucid dreaming is associated with increased activity in the frontal areas of the brain, areas which are already associated with higher order cognitive functioning.
So, what does this have to do with consciousness? It has been established that there is a marked difference between the two states of dreaming, however, the overall brain state remains the same. By comparing these specific differences in brain activity, the features that facilitate awareness can be highlighted and examined.