Wake-on-LAN is a standard that allows a computer to be turned on or woken up by a network message called "Magic Packet".
Amahi supports waking up devices that have a dynamic or statis static DHCP leases in your network, under Setup > Networking.
These devices some times come with WOL enable. In many PCs, they need to be setup properly by enabling WakeOnLan in their BIOS. This setting has quite a few names in BIOS's out there. Here's a couple of them <small>(find the one you need in the user manual of your motherboard/system)</small>: