Wake On LAN (also refered to as WOL) involves turning on a computer remotely over a network (LAN). Both your motherboard and NIC must support this.
The issue of plugging and unplugging your computer at home is a different issue. There should be an option in your BIOS whether or not to power up after the power has been restored after a power loss. If you could let us know your motherboard model, I could be able to help more.
ACPI stands for Advanced Computer Power Interface (or some mumbo jumbo like that). Basically, that means when your computer turns off, it will turn itself off when you tell it to shut down but it wont really be 100% off. Which is why you can WOL it, or WOR (wake on ring) which is to use a dial up modem and dial the phone number it is on and turn it on that way.
All these options should be able to be configured in your BIOS under ACPI/power manamgement.
As for that motherboard, it appears to be an ABit, but I cant find it anywhere on their site (abit.com.tw). Sorry
But you should be able to poke around the BIOS and play with those options.