A belief system is meant to be a comprehensive network of ideas about what one thinks is absolutely real and true. Within that system, everything is adequately explained and perfectly reasonable. You know exactly how far to go with your beliefs and when to stop your thinking. A belief system is defined by an absolute authority. The authority can be a text or an institution or a person. So it’s very important to understand a belief system as independent of religion. After all, Marxism and Nazism were two of the most powerful belief systems ever.
(Thanks to Adrian for this).