When designing for a system, the fact that is is interconnected makes it much more complex than something in isolation. This is kind of a trivial distinction to make, because just about everything designed is part of a system; in the real world, things are rarely in isolation. However, it’s much easier to look at a system in isolation, because it’s easier to calculate anything with fewer variables. This is where things get tricky. It’s easy to design a system such that it works in isolation. It’s harder to create something that will not fail when it’s used in unanticipated ways.
One example I can think of is through computer programming. In the debugging environment, you know what your program is capable of, and how it handles inputs. What happens, suppose, when a user inputs a string of text when your program is expecting a number? You, as the designer, must be able to account for that, so that it doesn’t crash when it’s in the user’s hands. This same idea applies to other areas of design.
One interesting thing to note is that nature herself is one huge interconnected system. Ecosystems are simply the interactions between systems of living things, with systems of, say, erosion, water cycles, etc. This system can catastrophically fail when say, a new species is introduced into an ecosystem not prepared for it (an invasive species). It just goes to show that nothing is immune. An environment evolves to be tailored to a specific niche, and something can disrupt it, because it wasn’t prepared for it.
Our goal as system designers is (obviously) to prevent these things from happening.