Awstats gives you valuable information like which file types on your server are getting hit the most, what page is getting the most hits, the number of hits you get from each search engine, search key phrases people are using to find you, and which sites are sending you the most traffic. All of this information is extremely valuable if you are going to have long term success with your website. Analyzing which keywords are bringing in visitors from search engines tells you what's working and what's not. You can then search Google and Yahoo using the key words to find out what your position is for those key words, which is a lot faster than doing random searches looking for your site.You can see how many times visitors are pulling up 404 Document Not Found Pages. This might show you that it's time to customize your 404 page with links back to your site. No sense in losing visitors.
You may be interested in knowing what type of browser your visitors are using. Awstats also tells you that. Another great thing about looking at your stats is that you realize which linking partners are the most valuable. This can help you decide which sites to try and obtain links from in the future. A well placed link can bring you a few hundred extra hits a month. One of the most important things you should be able to see from any statistics program is the amount of pages that the search engine spiders are traveling down your website. If they've stopped visiting your site, it may be an indication that something is very wrong. You don't want to get caught off guard one day and find out your site has completely disappeared from the search engines.