Just a little tidbid to add to delluser1's reply, if I may.
Some PSUs have not "upgraded" to the full 24-pin connector to keep compatible with older motherboards that might not have the extra 4-pin space around the ATX connector to handle a fixed-size connector. So, manufacturers allow the new 4 pins to detach, so you don't end up with a perfectly good PSU and motherboard not being able to work together.
Keep in mind that, even if the PSU doesn't have a 24-pin (or 20+4 pin) connector, but only the standard 20-pin + P4 connector (it should be VERY rare these days), 24-pin motherboards are able to properly function with older 20-pin PSUs. I've done that myself in the past, you just need to take care NOT to overtax your motherboard with high-drain components (like high-end GPUs, especially more than one).
Oh, and don't worry, the 20 and 24-pin ATX connectors are keyed, you can't have a motherboard meltdown by incorrectly plugging in the connector. Do keep in mind that the P4 and "+4" connectors ARE interchangeable but NOT compatible, though. Luckily, they ARE color-keyed (P4 is yellow+black) and you can't usually strech the "+4" lead to the P4 connector...
Hope this helps.
Miguel