Visualization of data is often needed in order to understand what the data means. When data needs to be visualized automatically, I often use the graphviz tools. Not that they are extremely pretty, but it works very well and is made to be automated.
Let me give a few examples of when visualization helps...
In SELinux, there is the notion of domain transitions: security contexts that can transition to another security context (and thus change the permissions that the application/process has). Knowing where domains can transition to (and how) as well as how domains can be transitioned to (so input/output, if you may) is an important aspect to validate the security of a system. The information can be obtained from tools such as sesearch, but even on a small system you easily find hundreds of transitions that can occur. Visualizing the transitions in a graph (using dot or neato) shows how a starting point can move (or cannot move - equally important to know ;-) to another domain. So a simple sesearch with a few awk statements in the middle and a dot at the end produces a nice graph in PNG format to analyze further.
A second visualization is about dependencies. Be it package dependencies or library dependencies, or even architectural dependencies (in IT architecturing, abstraction of assets and such also provides a dependency-like structure), with the Graphviz tools the generation of dependency graphs can be done automatically. At work, I sometimes use a simple home-brew web-based API to generate the data (similar to Ashitani's Ajax/Graphviz) since the workstations don't allow installation of your own software - and they're windows.
Another purpose I use graphviz for is to quickly visualize processes during the design. Of course, this can be done using Visio or Draw.io easily as well, but these have the disadvantage that you already require some idea on how the process will evolve. With the dot language, I can just start writing processes in a simple way, combining steps into clusters (or in scheduling terms: streams or applications ;-) and let Graphviz visualize it for me. When the process is almost finished, I can either copy the result in Draw.io to generate a nicer drawing or use the Graphviz result (especially when the purpose was just rapid prototyping).
And sometimes it is just fun to generate graphs based on data. For instance, I can take the IRC logs of #gentoo or #gentoo-hardened to generate graphs showing interactions between people (who speaks to who and how frequently) or to find out the strength of topics (get the keywords and generate communication graphs based on those keywords).