This idiom means to tell somebody something that you know to be completely false or untrue. Unlike a white lie, which is often harmless or trivial, to 'lie through your teeth' is to do so deliberately, emphatically, and without shame. The force of this expression means that to accuse someone of doing so can lead to conflict. That's why you would generally only say it to, or about, a person you are absolutely certain is lying. As the video shows, this expression is common in both a social and professional context, and is similar to the phrases 'tell a pack of lies,' and 'a barefaced lie.'