They're talking about the literal translation, not the conceptual translation. They're also a little off.
Gratia literally translates to "grace". Exempli gratia, with exempli used in the genetive case, directly translates to "graced examples". More appropriate English would say "for the grace of examples", and a better, localized translation would say "for the sake of example". It's commonly translated to "for example" since that would be the most common phrase to communicate the concept in English.
All these years later and college Latin finally was useful.
Quod Erat Demonstrandum - what has been demonstrated. (Or something like that..my latin sucks) Oversimplification - "I have shown proof of the statements made."