What happens is this:
Whenever any complex piece of software like a browser is written there will be errors in the way it treats data.
In the case of a browser like Internet explorer or Firefox it means that if you're clever enough you can construct a web page that crashes the browser. If you're really clever you can then use this error (vulnerability) to insert some malicious code (exploit)
These errors may not be directly the browser - they could be programs like flash or Adobe reader that the browser uses to display content.
If you can get this into something like an advert that is posted to lots of different websites you can infect a really large number of machines.
Despite the obvious advice of having AV software up to date there are 2 other things you can do to help protect yourself against such attacks
1/ Make sure your browser is up to date with the latest fixes from the writers - as soon as such vulnerabilities are found they are usually fixed but you have to have updates switched on (this is normally the default) and accept any requests to update.
2/ Less well known - don't browse from an account that has administrator privilleges. If you've only one account it's probably got full privelleges over the full machine.
If a malicious program crashes your browser it then inherits full rights - it owns your computer!
Here's a site describing how to create a new user
http://www.howtogeek.com/howto/5261/beginner-geek-add-a-new-user-account-in-windows-7/