VOC stands for volatile organic compounds, which are present in most paints, adhesives, furnishings and carpets (amongst many other things). Essentially they are compounds that become a gas at room temperature, making the air you breathe hazardous to your health.
VOCs will even hang around for a few years once you've painted your walls, so you continue to breathe in the toxicity. That's the bad news...
The good news is that there are several options on the market for low or zero-VOC paint, so it's easy to make the switch to a more health-conscious type. I bought Olympic Premium's zero VOC from Lowe's, which is a convenient and affordable option. Just remember that if you have your paint tinted (i.e., you get a color), you need to ask for a low/zero VOC tint as well.
Look for pictures of my new (*VOC-free*) items in the next week or so. Here's a hint; if you're in need of a fabulous chandelier, you may want to stay tuned.