Viral marketing is marketing that's contagious. The marketing message spreads around the internet via word of mouth or attached to another message. The classic example is hotmail. They offered a free email service, but they included a "sign up for our email service" along with every message. Now they serve ads to their users as they log in and out to check their emails.
Another example would be all the Golden Palace stunts that you see. They do something that makes them "newsworthy" and people start talking about what they did. I think it's also called "buzz marketing" because they're trying to make a buzz.
Another example would be the beer.com virtual bartender. People think it's so cool/funny/interesting that they link to it from their websites or
blogs, or they email others to ask them to go see it.
That's probably a poor explanation, but it might help a little bit.