I recently got to know of this website AppSurfer where they actually run Android OS in a web browser. It's interesting and also sleek.
How does this actually work?
The only clue I could find is from their website where they state
Run Android Apps in the Browser
Stream apps to any device or platform, on demand
So, it appears they use some sort of streaming technology where the App runs in an Android emulator instance running in their cloud and the content of the display is streamed to the clients browser.
That would mean that technically, Android does not run in the clients browser. The browser just acts as frontend to an (emulated I guess) Android instance.