Looking at systems as a whole is an essential concept of complex systems and system thinking which contradict the classical analytical thinking most of us using today. In the base of this concept stand the realizations that due to the nature of unexpectedness in complex systems one can’t understand the system by understanding how the parts of the system are working. Since components of the system are interacting one with each other, their interaction needs to be taken into account as well.
This principle required us to stop breaking system to parts and try to fix elements in the system, as we are doing when we try to fix a machine. To understand and improve complex systems (any organization is a complex system) we need to understand the system as a whole. The way to get a holistic understanding of the system is to focus on interactions between system parts. The best way to do it as of today is to use system thinking to analyze causal loops, flows, stocks, delays, computer simulation, etc. You can find a good intro can here.
When you are looking at a system and interaction between the system’s element you also need to take into consideration if the current interaction works for all components in the system and produce good results. Systems (especially the one where people are parts of the system) have their dynamics that might look like a problem for you, but those dynamics are a result of natural emerged order, order that works for all system parts. Fixing these dynamics because you believe it is wrong might (and usually will) end up with results that you are not looking for.
In a nutshell, observe the system as a whole. If the system is functioning well, think twice if you want to improve it by changing dynamics and element in the system. Just make sure that the system is continuously evolving and stay away from equilibrium, emergence will do the work for you. If the system is not functioning well then consider changing it by using flows or causal loops.