That connector on the graphics card connects directly to your power supply. Unless it is fairly old the power supply should have one or more PCI-Express 6 pin connectors for use on graphics cards. Of course, your card only needs one. If the power supply doesn't have one, look at some of the extras that came with your graphics card. It might have come with an adapter to convert a couple standard molex connectors from your power supply to a 6 pin PCI-Express. If that didn't happen, you can still buy said adapter separately.
One thing though, if your power supply doesn't come with a 6 pin PCI-Express connector, it might be under powered for your new graphics card. I say, "might" because I don't know what power supply you have (brand, model and max wattage).