Google Analytics is free and hugely powerful. It is designed to measure and analyse website performance and give you valuable insights into you website traffic and marketing effectiveness. It presents valuable information to you in a graphical format on how your website is performing and what your website visitors are doing when they are on your website.
Google Analytics will also allow you to measure the effectiveness of some traditional marketing campaigns by analysing visitor traffic and where your traffic is coming from.
Google Analytics allows you to identify how your visitors find you. It will tell you what websites your visitors have found you on (great for measuring the cost/benefit of your Yellow Pages website listing!).
Google Analytics will also tell you what keywords people putting into the search engines to find you.