An oath is a promise calling upon a item that the oath maker considers sacred (in this case God) as a witness to the binding nature of or the truth of a statement.
In the court room we, as citizens, are asked to swear "Under God" in order to validate what we say as true. This not only holds any validation, but it does not make any sense for someone who does not hold any "God," or perhaps a different God sacred.
Not only does it just not make any sense, but it goes against the Establishment Clause of the First Amendment to the United States Constitution.