A system is a concept describing a coherently organized arrangement of related elements with emergent properties not found in any subset of those elements and which collectively is defined by its function or purpose in a larger system of which it is a part.
Everything is a system. The elements of systems are systems. Systems may be abstract or concrete. The elements of abstract systems are concepts. The elements of concrete systems are physical objects. The boundaries of systems are a function of the perspective and purpose of their observers.
A system is a "set of elements or parts that is coherently organized and interconnected in a pattern or structure that produces a characteristic set of behaviors, often classified as its 'function' or 'purpose.'"1
"Systems are the set of all relationships that affect and are affected by the pursuit of a purpose."
You see the 'all relationship 'gets us out of just those things we control, into all those things which we can't control but affect our purpose. The 'affect and are affected' get us into the essential reciprocal nature of systems, which is why the base unit of system is not a part or an element but a relationship between parts or elements.2
"A system is a whole which is defined by its function in a larger system of which it's a part.3"
ISO 42010: "The Standard takes no position on the question, What is a system? In the Standard, the term "system" is used as a placeholder – e.g., it could refer to an enterprise, a system of systems, a product line, a service, a subsystem, or software. Systems can be man-made or natural. Nothing in the Standard depends upon a particular definition of system. Users of the Standard are free to employ whatever system theory they choose. The premise of the Standard is, For a system of interest to you, the Standard provides guidance for documenting the architecture of that system."4