If I want to do something extra when a particular configuration field for my custom module is saved (over and above saving to the Magento core config table), I can just specify
You need to tie your observer method to a specific Magento event (you can add your own, but need to find when you want it to be fired and add your own dispatchEvent call). If Magento has an event built in, use that event name in the config.
There's a pdf of the built in event lists on the web - google for it & you'll find it.