Beginning with some experiments performed by Stephen LaBerge in the 1970s, evidence began to appear showing that lucid dreams take place during REM sleep. Subsequent experiments performed were able to confirm this evidence and also shed some light on other psychophysiological aspects of lucid dreaming (LaBerge, 1990, ¶4).
In one early study, subjects were asked to move their eyes (during REM sleep) in specific ways when they realized that they were dreaming. These eye movements were recorded on a polygraph, and the results proved that the subjects were truly lucid while they were sleeping.
LaBerge then conducted some more experiments on dreamers, and thus learned that the physiological effects of the waking and dreaming states are almost the same. For example, the duration of time and the control of respiration were almost the same, actual muscle jerks corresponded to those muscles used in the dream, and most physiological responses to sexual activity were almost identical to those of the waking state (LaBerge, 2004, p.19).
Research has also shown that higher brain activation is necessary for lucid dreaming, especially during the first 30 seconds preceding and following the onset of lucidity, and that eye movement during this period is almost always above average (Brylowski, 1987, ¶3-4). Brain mapping technology has allowed researchers to see the distribution of brainwave activity in different states, and the consensus seems to be that if there is less Alpha wave activity in a particular region, then it is more activated (¶17).
Other studies have shown that it is necessary to have an elevated central nervous system activation level in order to have a lucid dream. There is a high level of cognitive function involved in lucid dreaming which requires a high level of neuronal activation. Also, a certain level of working memory is required in order for one to realize that s/he is dreaming, and the capacity of working memory corresponds to cortical activation, and this level of cortical and cognitive function is available only during the phasic (more active) REM portion of sleep (LaBerge, 1990, ¶22).

The result of these studies shows that what one experiences during REM sleep is the effect of neural activity that affects people's bodies. This helps to explain why people often think that their dreams are real. With regard to neural activity, dreaming about something and actually experiencing it is virtually the same thing (LaBerge, 2004, p.20). Some studies have even shown that people were able to help alleviate physical ailments such as menstrual cramps and hives through the use of lucid dreaming (Gackenbach, 1988 ¶25), and this leaves us wondering the extent to which one can actually use lucid dreaming to heal his or her own body.
References
Brylowski, Andrew and LaBerge, Stephen. (1987). Proceedings from the second annual lucid dreaming symposium session 1: what is a lucid dream: psychological and physiological considerations, EEG and other physiological findings [Electronic version]. Lucidity Letter, 6(2). Retrieved February 18, 2007, from http://www.spiritwatch.ca/Issue6_2/LL6_2_LaB_Bryl.htm.
Gackenbach, Jayne. (1988). The potential of lucid dreaming for bodily healing [Electronic version]. Lucidity Letter 7(2). Retrieved February 18, 2007 fromhttp://www.spiritwatch.ca/Issue7_2/LL7_2_Gackenbach.htm.
LaBerge, Stephen. (1990). Lucid dreaming: psychophysiological studies of consciousness during REM sleep [Electronic version]. In Bootzen, R. R., Kihlstrom, J.F., & Schacter, D.L., (Eds.) Sleep and Cognition (pp.109-126). Washington, D.C.: American Psychological Association. Retrieved February 18, 2007 from http://www.lucidity.com/SleepAndCognition.html.
LaBerge, Stephen. (2004). Lucid Dreaming: A concise guide to awakening in your dreams and in your life. Boulder, Co: Sounds True, Inc.