Most motherboards now have a 24-pin power supply connector. If you haven't already found a diagram showing the pinouts of the 20- and 24-pin power plugs, here's one borrowed from a handy site:
The two plugs are essentially the same, but the 24-pin version duplicates some voltages on the extra pins. The extra pins in the larger connector were meant to provide extra current paths for voltages that see heavy loads from newer processors and motherboard circuitry. Depending on how a motherboard is designed, it might work with a 20-pin plug connected (leaving pins 11, 12, 23 and 24 empty). But typically if the board has a 24-pin connector it needs the 24-pin power supply plug.
Most power supplies have a 20-pin plug with a separate 4-pin section that fastens to it for connection to a 24-pin mobo connector. It typically has one side designed to slide onto the end of the 20-pin plug, essentially turning it into the 24-pin version. This added plug does not have a retaining clamp on its side, so you can tell it from the the 4-pin CPU power plug. The wire colors are also different. For reference, here is the processor power plug, from the same website:
New motherboard specs call for the separate processor power connector for the same reason the extra pins were added to the power supply connector: to handle the high currents needed by increasingly faster CPUs.
When the motherboard has these connectors, you need to use them all to get everything working. Hope this helps. Thanks to smspowersupply.com for the diagrams, and thank you for using Fixya.