One thing you always want to do is to track the progression of your website. It is always going to be a good idea to monitor your websites performance after some updates or recent changes to see the effect they had to your visitors and to your overall website.
There are many scripts and software’s available to allow you to monitor your website. I personally use Google analytics and Google webmaster tools. Once you verify your website you are giving a treasure trove of information which you can use to quickly and accurately see how visitors interact with your website. From your analytics account you can see everything from where they came from, how long they stayed, and even which pages were most popular. How is this information really useful? For a start you can begin to identify weaknesses on your websites infrastructure and can begin to implement changes to correct them. Some pages which had low visitor popularity or pages which visitors tended to exit the site from could tell you that you need to focus on these pages as your visitors are telling you something by their actions and interaction with your site.
You will also be able to do the normal things you would have expected such as keywords used, location, browser stats, screen resolution used, and much more.
Is this a bit too much information? In a word, yes, but consider this. I know of this one site who was getting lots of visitors to his site, he didn’t think he needed analytics. Once they had a good look around their sites stats they discovered some large loop holes they missed, such as a staggering 25% of their visitors were accessing their site from a mobile phone. Using this information they were able to develop their site with the new information acquired.