If you are using FTP, for example, your computer is using Port 21. If you are using Telnet your computer is operating Port 23. If you use your web browser, you are using Port 8080. This port is always open when you are online. When you have a port open, it is vulnerable to attack.
Nuke programs ask the attacker to specify which port they wish to attack.
So if your attacker sees you on IRC and decides to nuke you, he or she opens their nuke program, which asks for a Port number and the IP number of the target. The attacker types in Port 139, or Port 8080, or any other port number, and the target's IP number, and then clicks the Nuke button. Nuking is NOT an IRC attack, since it does not use the IRC servers or network. But it is common on IRC because that is an easy place to obtain other people's IP numbers. When people are nuked they often worry that they are being attacked by someone with superior computer knowledge than they have.