It has previously only been possible to cast a browser window from Chrome onto a Chromecast by using a browser plugin for the Chrome browser. For people who want to cast their browser onto a TV or similar, these days are soon over, according to a Google+ post. The feature will be built directly into the Chrome browser in the future, eliminating the need to install a plugin.
If you have a recent version of Google Chrome installed, you can try this today, though the feature is still experimental. By going to chrome://flags/#media-router and enabling the “Media Router” flag, The Google Cast extension will then be disabled, and you will be able to right-click on a page and see a new “Cast” menu. Disabling the flag, will restore the extension.