Much like any other extract, this is simply root beer flavoring. It is a consistency sightly thicker than vanilla extract. Use root beer extract in recipes where you are looking for a root beer flavor, or use it to brew your own root beer. It can be mixed directly with cold water for a "flat" root beer, or brewed to obtain the carbonation.
Root beer extract is a specialty item, and is not traditionally found in an average grocery store. The easiest place to find the root beer extract is in a homebrew shop. Internet homebrew suppliers are a fantastic place to start, and a small bottle (1 oz.) will run about $4, and it will last you a long time. I hear rumors that it can be found in fancy bake shops, but I've never seen it, so don't say you heard it from me.