First and foremost you may want to read the official documentation.
Initially it is useful for animators, when you press the "I" key to enter a key, you can choose in several default lists of keys. Keying sets are just that, lists of properties. Instead of using the prefab list you can build your own. You do that with RMB pop-up menu when the pointer is over a property (Add to Keying Set).
Since the Blender user interface is not as customizable as we wanted, we are re-using this feature in our Add-ons to easily select properties.
An added bonus is that Keying Sets can be stored as textfiles, thus you can re-import them in a new project if you often use the same.
You can easily add/remove some properties in your Keying Set via the Scene panel. As explained in the official documentation there are some + and - buttons for that, in the "Active Keying Set" zone (near the middle of the panel).
Currently, there is a bug in Blender preventing the properties of the node editors of Cycles and the Blender Internal Engine to be added properly in a Keying Set. It has been reported (see: https://developer.blender.org/T44453).