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 that 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:
… a hierarchical associative array containing data to be rendered and properties describing how the data should be rendered.
Simple, but powerful.
One of the principle reasons behind having render arrays is that they allow Drupal to delay the actual rendering of something into markup to the very last moment. In Drupal 7, often-times as module developers, we would call the actual rendering service on an array in order to turn it into markup,for example...
