SavedVariables

What are they?
This is the name given to data which is saved by the user interface and addons between play sessions, storing things such as configurations, collected data, etc. Saved variables are stored in several different files:

All under X:/World of Warcraft Install Dir/WTF/Account/ACCOUNTNAME/:
 * ./SavedVariables.lua - only contains settings for Blizzard's own UI
 * ./SavedVariables/ADDONNAME.lua - global data, per AddOn
 * ./REALMNAME/CHARNAME/SavedVariables/ADDONNAME.lua - per-character data, per AddOn

The format of these files is plain LUA script. In theory, you could put actual code in them and have it be loaded, but it would be overwritten the next time variables are saved.

Beware, if you have a copy of the SavedVariables.lua in other locations than the correct one (specifically in your World of Warcraft directory, but possibly not limited to it), then it will be loaded INSTEAD of the one in your account, yet the account one is saved upon logout. This gives the appearance of all addons forgetting their configuration, and can be solved by renaming or deleting the errant copy.

Resources
There are numerous resources relating to saved variables:
 * Saving variables between game sessions
 * The TOC Format - Description of the .toc file format