The answer is that signing into Chrome allows you back up your account information to Google's servers. The benefit of this is that when you sign in to Chrome from another location (say, on your home computer instead of your school computer), you will continue to have access to all of the sites that you have bookmarked, your browsing history, or that cool extension that you downloaded at school (but now forget the name of). Google will even sync your saved passwords (if you give it permission to - personally, I prefer LastPass because I think it is more secure). Bookmarks can even be shared between your mobile devices using the Google Chrome browser and your desktop/laptop devices, so when you're on the road and come across a great site with your phone, simply save it to your mobile bookmarks and quickly find it when you return to the full browser.
In the short screencast below, I'll take you through the steps of signing in to the Chrome Browser. I've done it using my YRDSB Google Apps for Education Account, so some viewers may see an extra single-sign-on step that you won't be asked to complete.
Imagine, no more working to find the perfect site on the weekend only to forget what it is on Monday and no longer be able to find it. With your synced bookmarks and browsing history, it should be a snap!