There's a bit of disagreement regarding the history of the word "Barbecue." There are numerous variations on a few basic historically possible origins, and there are several wild and unlikely possibilities as well. Here are a few of the more common possibilities:

1. The West Indian (Taino Indians) word of "barbacoa" that means to cook slowly over low heat on a rack of wood
2. A French or Louisianan phrase of "barbe a queue", meaning to cook an animal from "head to tail".
3. That BBQ comes from 1800's advertisement for a combination whiskey Bar, Beer hall, Pool hall, and Pig Roast (Bar-Beer-Cue-Pig or BBQ Pig).
4. The brand on the cattle at a very hospitable Texas ranch had a "BQ" with a "bar" under it -- the ranch hands would eat the cheap cuts of meat (brisket) from the "BAR B Q" steer.
5. Derived from a word from an extinct tribe in Guyana that cheerfully spit-roasted their captured enemies.

I have a favorite among these, but it seems that nobody really knows!

But the art of Grilling (Barbecuing) is not just an American thing. It has roots in Asia, Europe, and Africa. So check out a bit of grilling's history here...

American BBQ -- the "classic" and the most comonly copied style of flavored grilling

World Variations -- the different tates of grilling and barbecuing from around the world