Putting a rabbit on his back and watching him seemingly completely relax is often called “trancing”. The state the rabbit is put is part of a bag of instinctual tricks to escape a predator. When a rabbit is grabbed by a predator the rabbit will “freeze” and imitate prey that has been killed.
By doing this the rabbit will boost it changes of escape and fatal injuries!From the scientists’ perspective, this is called “Tonic immobility” or just “TI”. It is considered to be a fear motivated defense mechanism. When the predator drops the supposedly “dead” rabbit or just relaxes it's hold a bit, the rabbit will burst to life and try to escape!
Some people put their bunnies into “trance”. Especially since this position makes clipping nails, checking the body and head for abscessed and other problems easier. It is a useful way to restrain the rabbit for a few minutes.
It is recommended to only do it once a month though, so be careful!