A system is a set of interconnected things / people / beings (whatever!) interconnected in a way that generates its own pattern of behaviors.(1)
What do I mean by "generates its own pattern of behaviors"? I mean that in a sense, a system is "alive." The roots for how a system operates are found within the system.
Here is an example. Hold the top of a slinky toy with your left hand. Let it fall on your right hand. Then quickly remove the hand. What happened?
If you did this right, the slinky bounced on the floor a few times.
Now think about it - did your hand cause the slinky to fall and bounce?
Not really. The slinky fell and bounced because of its own components. The slinky is a system.
Even if an outside event triggers a behavior, this event when applied on a different system might achieve different results.
(1) Donella Meadows, Thinking in Systems, 2008.