Easy WOL provides simple and clean interface to send "Magic Packets" to any device on your network. If your Android device (where the app is installed) is connected to a WiFi on the same network as the device you are waking up, all you need to provide is device's MAC address. The app will figure out broadcast IP address for the network and issue WOL over Broadcast. Obviously your device must support WOL. Sometimes Wake-On-LAN feature needs to be enabled in BIOS.
To wake up a computer over WAN, in addition to the above requirements, you also have to provide your router's IP or DNS address. The router must be configured to forward WOL packets to your local network. This is not always straight forward or even possible. All depends on the router you have and its capabilities. On some routers forwarding UDP port 7 or 9 to your network'a broadcast address works. Sometimes you may need set-up MAC to IP, or MAC to ARP reservation.
For more information on how to implement check here.
Required Android version: 4.0 and up.