It's when something (like tissue or an organ) is not where it is supposed to be in the body, literally "to fall out of place." So when someone says their chameleon has an intestinal prolapse it means that part of their colon has come out the vent. And in the case of a hemipenal prolapse, for example, one or both of the chameleon's penises have become stuck outside of the body. In the case of Daedalus, a bit of intestine was protruding from his vent, it became very swollen, and needed a vet to put it back in and add a stitch, to keep it in place until the swelling went down.
One culprit of intestinal prolapses is parasites. Another is probably dehydration and straining to poop, they probably push out their own rectum because they are too dry to pass fecal matter properly. Some think severe stress might cause them as well but this seems more like a guess.
With hemipenes it's usually just that they stick out one or both penises and they might become swollen from rubbing on a branch or from breeding and they become too enlarged to go back in on their own. They'll stick their hemipenes out sometimes just for fun, so in this case don't freak out just yet - but if they can't pull them in after a while they may need assistance.
It's a good idea for a vet to assist with both scenarios, and in the meantime it's vital to keep the tissue moist with something like a water-based lubricant.
