Chrome is the free browser created by Google. When using any of the Google Apps, use the Chrome Browser, since the apps maintain 100% of their functionality in Chrome (in some other browsers, you lose features). In addition, Chrome has consistently been rated as the fastest web browser.
For more information, check out the tour of Chrome Browser Features.
Extensions are extra features and functionality that you can easily add to Google Chrome. By using extensions, you can customize Google Chrome with features you like, while keeping your browser free of things that you don't use.
Check out the video below or go to the Chrome Web Store to find interesting extensions. Once you find something you like, install it to try it out.