Standard web statistic packages compete based on who can offer the most statistics, the most colorful graphs and trying to wrap usability around all that information. The guys at Crazy Egg have taken a different approach where you can measure and actually see what your users are doing when they visit your site, and from these results you can immediately optimize your site based on your visitors usage patterns. The result is that you can learn a lot more about your visitors from a lot less information that is found in analytics packages.
The above screenshot shows the heat overlay, which is where users are clicking and focusing their attention. Other parts of the application will show you where users click, and how many times.
The aim of Crazy Egg is for webmasters and site owners to learn from visitor usage patterns and improve their site based on what they learn from the application, as opposed to having page after page of statistics. Some features currently in development will allow users to track ad performance so that ad campaigns can be refined, RSS integration and demographic information of your visitors (filtering the map based on which visitors you wish to see).
The competition at the moment has similar services but targeted at large corporations (such as the site optimization services from Atlas), Crazy Egg delivers this kind of technology and tracking ability down to a simple level so that any body can use it and more importantly so that most people can afford it. It is very simple to understand, implement on your site and the results are stunning. Another site promising optimisation tools, probably not as cool as the heat overlay in Crazy Egg, is Map Surface - which is currently in a private beta.
Most site owners now are probably tracking conversion rates and looking at statistics, but when it comes to trying to enhance those results it is often trial and error. This is the situation I have been in for a long time now, but with Crazy Egg I can see what my users are doing and learn from that then optimize my site accordingly.
Pete Cashmore at Mashable also reviewed Crazy Egg a few days ago.