Basically, it means the card needs the extra power from the extra 4 pins.
IIRC an ATX 2.0 PSU has 24 pins instead of 20 for the connection to the motherboard. I think it needs support for the 6-pin PCI-express connector, too.
I'm actually using a 6800GS with a 20-pin PSU on a board that should use 24-pins, but it's run for around 2 months fine. I believe all 6800GS's have a slot for a 6-pin PCI-express power connector. If the card comes with a 4-pin-molex > 6-pin adapter, you should be fine even if you have a 20-pin-only PSU. You can buy one for cheap, too.
Just make sure the PSU pumps at least 400W for best results.