Some applications require what is known as WebView, a mini browser for functions like approving logins from Facebook and Google+. This is essentially a miniature version of Chrome.
It used to be that WebView only updated with the OS. In Lollipop, Google detached it from the Core OS in a way, and added the functionality for it to be updated via Google Play, like other apps, automatically. This allows it to keep up with Chrome and provide a better browsing experience.
The next time you log into an app and you are brought to a Web Page in the app saying "Allow 'The App' to assess your Google Account" or what not, see if you get get to the Google homepage via the "About Google" link. Then search for and open http://WhatBrowser.Org You will see how it is a mini chrome-based browser inside the app, provided by the system, and updated by Google Play.
Having this installed will keep it updated. You will not have to wait to upgrade the Android OS.