If your doctor says your sickness is endogenous, he means that whatever's wrong with you went wrong inside your body, and wasn't caused by anything you can catch, like a virus. Endogenous is a fancy term for anything that originates internally.
You're most likely to see the word endogenous when you're dealing with biology, but it can mean "coming from within" in other senses too. Use it for anything that originates inside a system. The revolution in your school was endogenous, even though the principal, always in denial, chose to blame it on outside rabble-rousers.