For the first time, scientists have recorded from individual brain cells during the dreaming phase of sleep.
They suggest that these well-known flickering movements accompany a "change of scene" in our dreams.
The recordings were made from patients with electrodes implanted in their brains to monitor seizures.
"It's a unique opportunity to look at what's happening inside the human brain," Dr Yuval Nir, from Tel Aviv University in Israel, told the BBC. "We're very thankful to the epilepsy patients who volunteered to take part."
Dr Nir worked with colleagues from France and the US on the study, which is published in the Nature Communications journal.
Over the course of four years they worked with 19 different patients, recording from electrodes in several different brain areas but largely within the medial temporal lobe.
This is not a part of the brain directly involved in vision, Dr Nir said.
"The activity of these neurons doesn't reflect image processing. It's more about signalling to the brain about a certain concept. You can close your eyes and imagine Queen Elizabeth, and these neurons will fire. This activity implies a refresh of the mental imagery and the associations."
When the patients were awake and shown a picture, especially one associated with a memory, the researchers saw a particular pattern of activity.
"About a 0.3 seconds after the picture appears, these neurons burst - they become vigorously active," Dr Nir explained. "This also happens when people just close their eyes and imagine these pictures, or these concepts."
Intriguingly, he and his colleagues spotted a "very, very similar pattern" during sleep. In particular, these bursts arrived just after eye movements during REM sleep.
This is the phase of sleep in which we dream, and it is characterized by these occasional, very quick eye movements.
It has long been thought that these movements might reflect the visual component of dreams, but there has been no clear evidence for this - until now, Dr Nir said.
"We are intimately familiar with the activity of these neurons. We know they are active every time you look at an image, or when you imagine that image. And now we see them active in a similar way when you move your eyes in REM sleep, so it becomes very probable that the eye movements represent some type of reset, or 'moving onto the next dream frame'.
"It's almost like when I was growing up and we had slide projectors. You move to the next dream slide, if you like."
"Even people who are congenitally blind... can still dream about their aunt coming to visit from Florida: her voice, the emotions and all the associations that go with that.
"And when the dream changes from meeting this aunt to, say, taking your dog for a stroll in the park, then the brain activity changes and this happens in sync with eye movements."
Other sleep researchers welcomed the findings. Prof Jim Horne, who established the Sleep Research Centre at Loughborough University, said the study fits with our improving understanding of REM sleep.
He also emphasized that flickering of a dreamer's eyes, which only happens in brief spurts, does not mean they are surveying a scene.
"The eye movements are not actually scanning your dream - they're reorienting your visual thoughts," Prof Horne told BBC News.
"This study endorses other findings that REM sleep has many similarities to wakefulness. I see REM sleep as rather like the screensaver on your computer; all you need is the touch of a button and your computer leaps to life. It's very close to wakefulness. Non-REM sleep is more like when you switch your computer off, and waking up requires a process of rebooting," he said.
Prof William Wisden, a neuroscientist at Imperial College London, was also convinced by the similarity of brain activity between awake and REM states - but he said there are bigger questions still to answer.
"The most fascinating question of all is why do we have to have REM sleep? Why does our brain have all this circuitry to do that?This paper doesn't answer that, but it does emphasize how similar being awake and in REM sleep are, for particular circuits in the brain," he concluded.
One of the popular theories to LOST was that it was part of an elaborate dream sequence, whether it was an individual creating their own sleep fantasy world, or a collective dream by networking the sleep cycles of patients together to form an interactive video-like game, or a laboratory experiment in human behavior where stories, characters and the like are feed back into the subjects who use experience it as a vivid dream.