In this Doc the terms used in the App will be explained.
Code Rules are specific actions that are being run over your code. For example, there's the Code Rule Trailing whitespace which can be set to the value remove. When this Code Rule is setup, it will remove all the trailing whitespace from the lines in your code.
In the PHP Code Rules section all the existing Code Rules are explained in more detail.
When referring to 'authorization' it usually means permission from GitHub. CodeOversight needs permission to your Git repository in order to make changes and create pull requests.
A build is being created as soon as a pull request has been made to your hosted repository. Basically, a build is the process of where CodeOversight is analyzing the code and applying the Code Rules.
Watched repositories are the repositories that you've connected to CodeOversight. Whenever there's a change on one of these repositories, CodeOversight will be notified and start creating a build for it.