How does Android WebView Update from Google Play work?
It means that applications that use the WebView class (for displaying a web page within an app, basically) will now use the Chromium version of WebView and thus render things the same way Chrome does, rather than the old way.  This also allows it to be updated so that any rendering/other errors can be fixed, instead of you permanently being unable to see/use certain pages or elements within WebViews.

And yes, the old Android browser has been replaced by Chrome as the default bundled with Android.