"e.g." is an abbreviation of the Latin "Exempli gratia lit," which means "For the sake of example." This type of example is not specific or limited in scope, i.e., anything that is an example of what is being talked about is fair game. Aside from discovering the differences between the two in some of my English classes, I got a "Latin Calendar" for Christmas this year, and this is one of the phrases that came up.
One time, a teacher told me that e.g. meant "examples given" or roughly "examples follow." This is not a bad way to think of it, as long as you remember that e.g. is really the abbrev. of the Latin above.