No, the two are not related, as far as I can tell. But Congratulations to Firefox (my personal browser of choice) for reaching 20% of market share. They reached the number for 2 out of 4 weeks in October. For a browser that doesn't come pre-installed on most computers, that's quite impressive.
The new privacy feature is included in a pre-release version of Firefox 3.1. It's called "Private Browsing" and you can turn it on via the Tools tab. When you do, it won't store data such as history, cookies, and cache. But it only prevents such storage for the browsing you do when the feature is turned on. To store that info again, just turn it off.
What Private Browsing does NOT do is keep you anonymous on websites or your ISP. It also is not a security tool to prevent spyware downloads and such.
A good use of the tool is if you're looking online for Christmas gifts but you don't want your husband to find out what you're getting him! (Just make sure to take note of the things you want to remember.)