It looks like Gmail engineers are experimenting with push desktop notifications in Google Chrome and Gmail. This is a long-awaited feature of web browsers, and will allow web applications to act more like traditional desktop applications. As more applications become web-based, ditching the traditional fat-client pieces, small things like this will help users with the transition.
Is the new option showing up in your settings? (Click on image for full-size.)
Here’s a full explanation from the official Gmail blog.