The primary advantage of mouse gestures is, that you can keep your hand on the mouse. Thus, you lose no time switching between the mouse and the keyboard, which is annoying and slow.

Especially for viewing websites this comes in handy, because you usually don't need to type text anyway. And with a scrollwheel-equipped mouse, the user experience gets even better. All the usual actions, such as following a link, reloading a page, go back/forward in the history, close a window, open a new window, etc. can be performed while keeping your hand on the mouse, ready to click on links. Also, it helps one handed surfing.

You can get mouse gestures working in Mozilla (as an installable module) thanks to the Optimoz project. Using JavaScript, you can configure Mozilla's handling of your mouse gestures, and you can add new ones. Like this one, that tells you How to search E2 using mouse gestures in Mozilla. Along with tabbed browsing (also pioneered by the Opera browser), I consider this the two best UI features of modern browers.

The cenceptual sister of mouse gestures is called pie menus, which also aid in the act of one-handed browsing but operate in a way more similar to that of a traditional menu in the ubiquitous WIMP system.