With just ten things to tell Moses, God included that in the list. Discuss what this commandment means to you. Non-Christians are welcome to chime in, their opinions matter as much as anyone else's.
false witness is aggressive thoughtlessness cranked up another level, and aggressive thoughtlessness is the only thing wrong with this world. that and hatred of logic. this is one of the better of those ten, that has universal and intrinsic merit and isn't just a cultural perspective of monotheistic belief.
Seems pretty straightforward. It means falsely accusing somebody of something, or falsely corroborating said accusation. One can see the damage that this can do in modern daily life, from false rape and corruption allegations to calling the cops to falsely allege assault because an African-American birdwatcher questioned a dog leash violation. It's Pizzagate and all the other fake news designed to smear political candidates. When God put it on the list, (S)he knew what (S)he was doing.