The term service management system is composed of three terms: service, management and system. The definition of a service management system is logically based on the definitions of those three components.
What is a system?
Without a doubt, Russell Ackoff was one of the greatest leaders in the Systems Thinking domain. He defined a system not as the sum of the parts, but as the result of the interaction of those parts:
"The essential properties that define any system are properties of the whole which none of the parts have. A system is more than the sum of its parts; it is an indivisible whole. It loses its essential properties when it is taken apart. The elements of a system may themselves be systems, and every system may be part of a larger system. ...The basic managerial idea introduced by systems thinking, is that to manage a system effectively, you might focus on the interactions of the parts rather than their behavior taken separately."
In proper English, we define a system therefore as a coherent set of components, characterized by the performance of that set and not by the characteristics of the components. In order to function properly, such a system must be efficiently arranged and the components must be a logically related set. If you want to learn more on the term 'system', you may want to study the great overview that Graham Berrisford has put online.
Details of USM's service management system are explained in the USM Wiki.