Here is a small introduction provided by Google into what its Analytics program really is:

What's Analytics?

Google Analytics is the enterprise-class web analytics solution that gives you rich insights into your website traffic and marketing effectiveness. Powerful, flexible and easy-to-use features now let you see and analyze your traffic data in an entirely new way. With Google Analytics, you're more prepared to write better-targeted ads, strengthen your marketing initiatives and create higher converting websites.

Google Analytics allows you mainly to keep track of who visits your website. You can:

  • analyze your traffic by country 
  • view your traffic sources (how someone gets to your site)
  • see how much time people spend on your site
  • see how many times each specific page is viewed
  • see the languages, browser and operating system, flash version, screen resolution [and more] of your visitors.

Click here to go to Google Analytics' official tour page 
Sign in to your analytics account here (using your Google account).