The name Automation covers the entire scripting functionality of Aegisub.
The single purpose of Automation is — as the name implies — to automate various aspects of subtitle creation and editing. This was originally used mainly for creating karaoke effects, but over time it has expanded in scope to support more general purpose macros which add arbitrary new functionaly to Aegisub.
Some of the goals of Automation:
Aegisub comes with several Automation scripts already packaged and ready to use. This includes the advanced Karaoke Templater script and a collection of macros to simplify some editing tasks.
Aegisub almost always has several Automation scripts loaded at a time. You can see what scripts are loaded, and load/unload more from the Automation/Manager window.
All Automation scripts also present themselves in Aegisub in one way or another. Some appear as macros in the Automation menu and others appear as filters in the Export dialog. Some scripts even appear in both places.
Automation supports scripts in Lua 5.1 and MoonScript. Other languages used to be supported, but no one used them.
There are several example scripts included with Aegisub to give you a head start on writing your own ones. A word of warning: Unless you are an experienced programmer the kara-templater.lua script is a very bad place to start!