WHAT IT DEFINITELY IS
Exodus 20:7 (NIV) - You shall not misuse the name of the Lord your God, for the Lord will not hold anyone guiltless who misuses his name.
I hope we can all agree that this is definitely a very specific (but possibly not clear) teaching on the kind of language that should not be coming from our mouths. We are not to misuse, or take lightly, the name of God (and since Jesus was also God, we'll throw his name in there with this teaching as well). The potentially unclear question here is what is really meant by "misuse" or "vain" as the KJV states.
Now, in the house that I grew up in, this meant never saying "oh my god", or using "jesus christ" as a swear, or putting "god" before "dangit" or "damn", or even saying "I swear to god". In other words, if you weren't specifically talking about God or Jesus, then their names should not be thrown around casually. I think this was and is an accurate teaching of that scripture. These uses definitely would be misuses, or show a lack of respect, of the name of God.
I've also heard it taught that this teaching was referring to using God's name in an oath when you're not serious about the oath. For instance saying, "I swear to God I will repay that debt," when, in fact, you have little intention of repaying the debt. I would say that this would also be misusing God's name, but that wouldn't mean that the first teaching is incorrect. I believe both would be examples of misuse.
There may also be other ways to misuse God's name. Telling someone a particular desicion was "God's will" when it was more accurately your own desire or opinion, would be misusing God's name. Let me know what you were taught about this scripture, if you agree/disagree, or other examples of misusing God's name.