To understand how browser based exploits work, you should understand how browsers work. I have found a nice detailed article about it. How Browsers Work.
Since each browsers have its own engines, the browser based vulnerabilities are specific to the browser( also even Operating system specific ) . An exploit code for Internet Explorer 6 probably will not work for Google Chrome, for example. In addition, if you search for more browser vulnerabilities, you will find out that the vulnerability platforms are changing. There are exploits work in only some Android versions for example. You can check out several vulnerabilities of Google Chrome as example; Google Chrome List of Vulnerability
Rapid7 MS10-002 Microsoft Internet Explorer "Aurora" Memory Corruption and
also from here: CVE-2010-0249