The 'System' is the 'Object of Interest' and 'The Surroundings' is everything else.
An understanding of System and Surroundings is such an important perspective of scientific research and development that every student should spend extra time learning of it's importance.
The 'System' is the 'Object of Interest' to be studied. Every experiment has a 'System' to be studied and evaluated. In chemistry the System can be the intrinsic nature of a chemical reaction, determination of structure of a substance, the physical appearance of a material object and so on. The issue that's most important here is the relationship between the 'System' being studied and the 'Surroundings' in which the 'System' is doing whatever it is supposed to be doing.
Confusing? Not really if one thinks of themselves as an 'Observer' within the surroundings and the 'System' as an object of interest/study sending signals to interpret about its nature and behavior. Einstein stated "In order to understand the secrets of the universe, one must first learn its language." That is, the object of interest (The System) is sending you signals in the form of a language that you - as a scientist/observer - must translate into a meaningful picture of what the system is all about.
Science in a general context exists because of how you, the observer, in the surroundings detects and interprets the signals sent by the system. The simplest example of how this works is the 5 senses of man; i.e., touch, taste, hearing, vision, smell. These are detectors of the language that an object of interest (The System) is sending. How you (the observer in the surroundings) interprets the signals received defines how one responds and connects to the object of interest. Basically, the entire essence of science is inventing and applying devices to detect signals sent by the multitudes of systems that are performing a symphony within the universe. This is what makes science most exciting; i.e., the detection and interpretation of the many languages (Systems) that are part of our everyday existence so that we can understand and connect to these systems and understand the very essence of our existence.
Great Question!! Thanks for asking. Doc