What is the purpose of a "Magic Packet Sniffer"?

With the help of a Magic Packet Sniffer you are able to verify if the wake-up signals (Magic Packet) were sent to the target computers.
The sniffers show you the incoming "magic packets".

You can find a link to the Link download the open source WOL sniffer.

Wake on LAN Sniffer
Wake on LAN Monitor: WOL Sniffer