Back in the days when Mad Men actually walked the earth, it was probably easier to explain exactly what an "advertising agency" did.
It's not quite as clear-cut anymore–a realization that usually hits me when I'm writing a proposal and trying to describe our capabilities without it sounding like we do everything but hang drywall.
It's not just that the Internet has changed everything (although it has). I think it's also that the arts of communication, marketing and advertising overlap more than they used to. Let's face it: every organization, large or small, public or private, is selling something. And every written, spoken, video, web or other communication that comes from an organization either contributes to that selling effort or detracts from it.