There are lots of definitions available for RBD and all pretty much say the same thing (some are just a little easier to understand than others!), but here's the general idea...
REM behavior disorder (RBD) is a sleep disorder first described in 1986. Dr. Carlos Schenck is credited for identifying RBD as a new category of parasomnia (a condition that occurs during sleep and creates a disruptive event), along with Dr. Mark Mahowalk, his colleague at the University of Minnesota and the Minnesota Regional Sleep Disorders Center at Hennepin County Medical Center in Minneapolis. They published their findings on RBD in the article "Chronic Behavioral Disorders of REM Sleep: A New Category of Parasomnia" which was published in the journal "Sleep".
There is no known cause for RBD. It is, however, known to occur during rapid eye movement (REM) sleep.
Patients with RBD act out and react to situations occurring in their dreams (which are often very dramatic and/or violent), during rapid eye movement (REM) stage sleep. It is similar to other sleep disorders that involve motor activity, such as sleepwalking and periodic limb movement disorder, but unlike these conditions, RBD movements occur during rapid-eye-movement (REM) sleep, which is usually characterized by a state of atonia, or sleep paralysis.
In a person with REM sleep behavior disorder (RBD), the paralysis that normally occurs during REM sleep is incomplete or absent, allowing the person to "act out" his or her dreams. RBD is characterized by the acting out of dreams that are vivid, intense, and violent. Dream-enacting behaviors include talking, yelling, punching, kicking, sitting, jumping from bed, arm flailing, and grabbing.
Normal sleep consists of a series of REM dream episodes. They occur about every 1 ½ to 2 hours each night. This means that an RBD episode tends to first appear at least 1 ½ hours after falling asleep. Episodes may continue to occur until waking up in the morning. Active RBD episodes may appear as many as four times per night. They may also occur as rarely as once per week or per month. RBD does not normally appear during a nap.
An RBD episode often disrupts the sleep of a bed partner. This is how a person with RBD may become aware of the problem. People with RBD are not more aggressive or violent than others when awake. RBD is a medical problem. It is a neurological disorder. It is not a psychiatric disorder. People with RBD do not normally have a mental problem.
Click on the photo below for REM Behavioral Disorder's Diagnostic Criteria:
And for a more in depth explanation of RBD and it's history, I recommend this article from the Sleep Review Journal by Theresa Shumard : Defining REM Sleep Behavioral Disorder.
The National Sleep Foundation also offers an easy-to-comprehend explanation here: REM Behavior Disorder and Sleep.
Update April 2018
3 months ago