All web servers write logs of every hit and every error (such as page not found) on your website. Most web hosts make these logs available to you. However, they are a little hard to read!
There are different programs such as AWStats that make very nice bar charts and graphs of your logs, including analysing where your visitors come from, which pages are viewed the most, even what the person was searching for in google that made them find your site!
You can use these statistics to see how your site is being used, and how it can be better.
Rule of thumb: If you are serious about your website, you want website statistics. All the statistics programs are good; it's just personal preference which one you might like.
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