Complex systems are assemblies of components that interact according to a fixed set of rules to form a unified whole. Systems theory is the study of complex systems and encompasses perspectives from multiple disciplines. By definition, all digital products are complex systems, so the perspectives of systems theory can shed light on the problems encountered in digital product management.
The key insight of complex systems is that the network of components within the system creates a situation where small changes to one component can propagate through the system and have far reaching impacts. Almost every developer and product manager has experienced this when a bug report comes in after releasing what was thought to be an innocuous change.
Systems thinking is an aspect of systems theory that focuses on the skill of solving problems or awareness of solutions to problems within the context of complex systems.
So, as a product manager it's important to understand and be aware of the potentially broad impacts that changes to the product and within the product's related systems can have. More important, more important than understanding the interaction of the components, is the understanding of the system as a whole.
You can analyze a system indefinitely, but the result will only be knowledge of how the system works, never why the system works the way it does.
"Why" is external to the system, yet it is central to a product. Why a product is, or will be, successful is independent of how it works, given, of course, that it does work.
This is the final responsibility of the product manager and their team, to understand why a product is the way it is, or why a product should be different. And this understanding will extend past the technical construction of the product to its relationship to the users and the business.