On November 13, 2012, we attended a Web Performance SF meetup in San Francisco. The concept of an Evergreen Web Browser was introduced by a core developer of jQuery, the plugin that is used by almost all web applications for cross-browser JavaScript.
An Evergreen Web Browser is a web browser that automatically updates itself on startup. It solves the problem where people don't check for or download updates to their web browsers and, thus, run a web browser with security holes and bugs. An Evergreen Web Browser solves this problem by updating itself and telling you about it. For developers, they won't have to support old web browsers.
Current versions of Firefox, Chrome, ans Safari are Evergreen Web Browsers - they automatically update on startup. Internet Explorer is not.
Evergreen Web Browsers, however, can give headaches to IT administrators. Some web applications or websites might work only with a specific version of a web browser and break in a newer version. Evergreen Web Browsers are also annoying when making a presentation. Basically, Evergreen Browsers are not for everyone all the time.
--
--
Correction: October 11, 2013
It appears that Internet Explorer 10 now comes with a feature that keeps it auto updated making it evergreen as well.
-Anthony Scherba