Website statistics allow you to view a wide range of detailed information about traffic sources, visitor locations, number of visits, referrals, social networking and advertising, just to list a few.
Each website I create includes an installation of Google Analytics. Information provided in this account over time allows you to easily get a good understanding of your main demographic, where the bulk of your visitors are being referred from and how many of these are first time or recurring visitors.
For instance, you may be receiving a lot of referrals from Facebook, but not many from Twitter. Knowing this, you are able to work on your tweets to help drive traffic to your website.