Wake on LAN is a standard for a motherboard to, when switched off, power an external device, which can then instruct the motherboard to switch on. While named 'wake on LAN', absolutely any device may be used, so long as it has a sufficiently low power requirement.

A WOL capable motherboard provides a WOL connector1 :

1 - +5v Standby
2 - Ground
3 - PME (Power Management Enable)
The +5v pin may be used to power the device - if the device has sufficiently low power requirements, it can be powered by the WOL header alone. Pulling pin 3 to +5v causes the motherboard to wake up (if it is not already awake). For WOL to work, the power supply must provide sufficient standby power to supply both the motherboard and any connected devices: while an ATX motherboard may only require .5w, a modern ATX with a WOL device connected may draw up to 10w. If the power supply is not designed for this, the motherboard may not receive enough power to turn on, and may even damage the power supply by drawing too much current.

In modern motherboards (PCI 2.2 or later), these signals are replicated on the PCI and Cardbus busses. A compatible NIC plugged into such a PCI or Cardbus slot does not need a cable for WOL functionality. PCI 2.2 provides 3.3v rather than 5v standby power, thus older 'cable style' WOL cards will not work without modification. Most PCI 2.2 motherboards therefore provide a WOL header for backwards compatibility.

While the standard is called 'Wake On LAN', the device plugged into the WOL header need not be a NIC, or even a card. Internal modems with 'Wake on Ring' use the WOL header to wake the motherboard. The WOL header is ideal for connecting homebrew devices to wake the computer up by other means - infrared remote controls, or powerline home automation devices, for example.

I cite:
"PC Infrared Remote Receiver", Silcon Chip Magazine :
"PCI Bus Power Management Interface Specification", Intel Corp. :

1 - Conversely, any motherboard with a WOL header is WOL capable. It is a common misconception that the motherboard must provide PCI standby power: in fact, the NIC is powered by the WOL header. In some cases, the NIC need not even be plugged into a PCI slot.