What constitutes a system? Any kind of organization of people, tools, or resources. It could also be used to describe the way something gets accomplished through a set of programs or services.
Systems come in various shapes or sizes. You may have a particular way that you take to work, or a certain method to loading or unloading a dishwasher. On the other end of the spectrum, a country's healthcare infrastructure would certainly qualify as a system, as would it's network of roads or even the power grid.
Working within a system to effect change requires intimate knowledge of the key points at which decisions or made or where the parts touch each other. It's also helpful to be able to see the whole. Moving back and forth between the macro and micro levels of experience, you can quickly test and see the impact that small changes can have on a system.
Changes to a system can come from the top down, the bottom up, or from within. However, lasting change is created when the stakeholders of a system are actively involved in shaping their future.
Where do you start?
Start with examining the big picture. What overall goal do you want to achieve? With this is mind, think about how your design will impact the local user, or a single individual. How will it impact a small group of users; a community of users; and then people not in your community?
Shifting from the micro to the macro perspective and comparing and contrasting what you see will give you a deeper sense of how a solution may actually work and whether or not it is consistent with your vision for your organization. When an idea is developed for a small scale application, and then pulled out of that environment and placed in a new, larger context, the inefficiencies are generally very clear.
A design solution should work well at both small and large scales to be truly effective. Once you get over this hurdle, scaling up a small idea to solve a systemic problem is much easier to accomplish.