Hi Dan,
The short answer is the red connector is to provide more power if your computer is having trouble recognizing the hard drive...it does not give you extra speed. Here is longer info from the FAQ section of this web site:

Power supply: Different computers and laptops deliver more/less power to the USB ports. (This information applies to 2.5 inch USB powered drives, not the 3.5 inch AudioPhile editions that use an external power source.)

* On one end of the USB cable, there is a second USB connector you can use for extra power (usually a little smaller than the main one). If your cable looks like that, first make sure you have the larger connector plugged into your computer. It is *normally* only necessary to use the one plug.
* If that doesn't work, try connecting the main plug directly to a USB port on the back of your computer, rather than a USB hub or ports on the monitor/keyboard/front of the computer case. Unless you have a self-powered USB hub (i.e. one that plugs into the wall, or battery-powered) it doesn't have any more current drive than is available on its usb connection to the mother-computer. So each single port on a hub often doesn't have enough power to drive some devices. USB ports on the front of your computer etc. can be similar to this.
* You could try connecting the extra power USB plug to another port (so you have both cables plugged in). Note that there is often a maximum current available per pair of vertically stacked USB ports, so you may have better luck bridging between two pairs. Also, if you have other USB powered devices that require alot of power, such as audio interfaces or a MIDI keyboard, it would be best if each of those had its own pair.