That's right, your website is hiding some valuable information from you. It knows who is visiting it, where they are going, and even more importantly - why they leave!
Understanding your websites traffic statistics, logs, and gathered information is like asking someone to blindfold you while you are driving.
Those statistics aren't really hiding, but a majority of webmasters don't use them because it's just a bunch of overwhelming numbers, that really don't make sense to them. If you have a Cpanel based host, most of the statistics you will ever need is at your fingertips.
I know the first thing I go for once I get in my website statistics is referrers, and keywords. I want to know where my traffic is coming from and from what keywords.
There are some things you want to see in your statistics, and some things you don't.
1.) "Stickiness"- You want to see people staying on your page for more than a few seconds. If you have a ton of visitors and none of them stay on your site for more than a few seconds, you have a problem and it's time to address it. Figure out WHY they are leaving, make those changes and then reanalyze in a week.
2.) Most Requested Pages- Your statistics can tell you the most requested pages. Those are the pages that visitors go to the most. The least requested pages may require some work or content added to increase their popularity.
3.) Entry and Exit pages - These stats will tell you what pages your visitors enter on, and what pages make them leave. Sometimes this can cause a problem. Here is an example: A few weeks ago a client wrote me and said they weren't getting any sales, although they had a lot of keywords based traffic. Well that keyword based traffic is a great thing, and their site was well organized and professional. The first glance didn't reveal anything wrong. After a few minutes of looking through the statistics I found that the Terms of Service page was losing a large amount of the visitors. We found some huge spelling and language errors. He wrote me a few hours after fixing these to report that he had an order already.
4.) Referral URLs- Pages that link to you are the best way to increase traffic and increase search engine traffic. Your statistical program will tell you what URL's are sending you traffic. It's also a great way to figure out if your linking partners are holding their end of the bargain.
5.) Keywords- It's a good idea to pay a lot of attention to this. If search engine traffic is the most common method for your traffic generation, it's probably your most important statistic.
Statistical programs tell you what keywords, and what keyword combinations brought visitors to your site. Hopefully they were keywords that are relevant to what you are trying to sell.