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...