There are two parts to ETOPS (tongue in cheek "Engines Turn or Or People Swim")..The first is the certification to design standards, including flight testing. The second, and perhaps more crucial element, is the operations/procedures certifications. In the first stage, the entire system (engines, airframe, fuel system and everything else) is evaluated as a comprehensive whole. Essentially, you're looking to eliminate single points of failure.
The second part is arguably more important as it deals with the statistical failure rates. The assumption is that a modern jet (turbofan) engine is highly reliable. As the basis of such procedures, multiple, similar failures are worrisome. An airline must have approved ETOPS operations to fly routes requiring ETOPS (a certified airplane is necessary but not sufficient). Common operational procedures include not replacing both engines at the same time, servicing similar fuel system components together, etc. Basically, avoid the possibility of introducing a single point of failure into otherwise redundant systems.