Render arrays also existed in the previous versions of Drupal and they were important to the theme system. In Drupal 8, however, they have become the thing—a core part of the Render API which is responsible for transforming markup representations into actual markup.
Acknowledging my limits as a writer, I will defer to the definition found in the Drupal.org documentation that best describes what render arrays are:
Simple, but powerful.
One of the principal reasons behind having render arrays is that they allow Drupal to delay the actual rendering of something into markup to the very last moment. What do I mean by this? For example, in Drupal 7, oftentimes as module developers we would call the actual rendering service (the theme() function) inside a preprocessor to "render" some data in order to print the resulting string (markup) in the template. However, this made it impossible to change that data later in the pipeline, for example, in another preprocessor that comes after the one that did this rendering.
For this reason, in Drupal 8, we no longer have to/should render anything manually (except in very specific circumstances). We work with render arrays at all times. Drupal will know how to turn them into markup. This way, modules and themes can intercept render arrays at various levels in the process and make alterations.
We will now talk about render arrays and the different aspects of working with them.