Understanding how your visitors interact with your website is a powerful tool.
Using analytics software, like Google Analytics, allows the collection of a wide range of analytic data, including visitor demographic, traffic sources, page visits, visitor numbers, referals, social networking and advertising, just to list a few. This data, can then be used to understand how visitors use your website, allowing you to adapt your content, or target new sources.
For example, 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.
As standard, I include the setup of Google Analytics on all of my web design projects.