This app allows to wake up computers and other devices that support the WOL (Wake On LAN) standard. Most modern computers do support this, however, you may need to enable Wake-On-LAN in BIOS and sometimes in network card driver preferences. Although the app itself is very easy to use some networking knowledge may be required to set up your devices, especially if you are walking up over the Internet.

To wake up a computer on your local network, all you need to provide is your device's MAC address. The app will figure out the broadcast IP address for your local WiFi network and send WOL packet to all devices on the network. Obviously, your iPhone/iPad must be connected to the same local network as the device you are waking up.
You also have the option to specify the target IP address manually. This may be required if your network router does not support local broadcast, when using VPN, and in some other situations.

To wake up a computer over WAN you have to provide your router or firewall's external IP / DNS address. You must also configure the router to forward WOL packets to your local network. Simple port forwarding is not always sufficient. It may require forwarding UDP port 9 to your local broadcast address, setting up MAC-IP, MAC-ARP reservation, or something similar. Not all methods work on all routers and some cheaper routers may not allow any of this at all. Refer to your router's manual or contact the manufacturer's support for more information.