IP-scanning, or portscanning, has to do with looking for open ports on computers. Every computer connected to the internet has it's own number, the IP-number. If you want to check any of this, you can use the number 127.0.0.1 - it's the number each computer assigns to itself (useful for testing stuff). Each computer has a bunch (256x256) ports, they are all numbered - if you compare your computer with a house, the IP-number is the housenumber, and each port is a door.

Processes or programs that use the network use one of these ports - so, by checking if a computer has a port open (a door unlocked) you can tell which programs the computer is running (and use that to your advantage). You can do this two ways - You want to know which ports are open on a specific computer: in this case, you want to scan all ports (check all doors) on one IP-address. You can also be looking for computers that are running a program - in that case, you scan a range of IP-adresses for one specific port.

If you want to check your computer for the ports you are using, open a dosbox (I'm assuming you're using windows) and type: netstat -a

If you want to scan other computers, you probably want to download a portscanner - you can find enough of those on the internet, use a search engine.

If you want to get a simplistic, but really clear view on how information is transmitted from your computer over the internet, I really recommend watching the movie Warriors of the Net - I showed it to some of my computer-illiterate friends, and they all got the idea pretty quick.