It is just what I have read here on curezone. Basically, the Epsom Salts draws fluid into the intestinal tract and that's what moves things along faster. Unfortunately, then there is less fluid in other parts of the body so you may become dehydrated if you don't keep drinking. Dehydration is hard on the kidneys. I have found that I get kidney pain after doing a Liver Flush even though I do drink lots of water. I think my kidneys are not as strong as others here who flush.
This is a very rudimentary explanation - hopefully someone will come along who can point you towards some research.