A system is a collection of elements or components that are organized for a common purpose. The word sometimes describes the organization or plan itself (and is similar in meaning to method, as in "I have my own little system") and sometimes describes the parts in the system (as in "computer system").
A computer system consists of hardware components that have been carefully chosen so that they work well together and software components or programs that run in the computer.
The main software component is itself an operating system that manages and provides services to other programs that can be run in the computer.
A filing system is a group of files organized with a plan (for example, alphabetical by customer).
All of nature and the universe can be said to be a system. We've coined a word, ecosystem, for the systems on Earth that affect life systems.
The term can be very useful because so many things can be described as systems. It can also be very unuseful when a more specific term is needed.