The spare 4 pin plug from the PSU you speak of goes into the 24pin ATX connector on the motherboard.
You must take the 20pin connector out of the socket and you will find the spare 4 pin plug will mate up to the 20pin plug.
It is then a simple matter of connecting your now 24pin plug into the motherboard 24pin ATX socket.
This simply provides extra power to the motherboard via a separate circuits when required by the motherboard and it's installed components.