Complex systems are all around us. In the technology world, we often pigeonhole the term to refer to our computer services, but the concepts of complex systems are much broader than that.
Anything that has more than one component with a behavior can be considered a complex system, from living organisms to political systems, from the cars that drive on our roads to the buildings that constitute our cities and towns. In fact, those road systems and cities are complex systems as well.
All complex systems are by definition difficult to understand because they also generally exhibit emergent behavior. Emergence is when a system exhibits behaviors that you could not possibly infer from its component parts and which only come to be when these components are working in unison.