They can build it in many different ways. There are different elements to what the cloud computing model is and there are more detailed technology discussions, but you can pretty much build whatever you want.
You could build Netflix on a cloud-based model, which has you being able to secure payments for whatever you're about to watch. It is completely cloud-based. So, yes, it can run the gamut of running a business on various elements, including enterprise resource planning software. It is available in the cloud on a pay-per-use basis.