Stats supplied by your host are derived from your web server log files. These stats will overestimate your traffic for the following three reasons :
If someone loads an image (or any non-HTML file) from your site without loading an actual web page the server logs will count a visit regardless. Since the visitor did not actually make it to your site 123Stat filters these events out and no visit is counted.
If a robot, spider, or any automated process loads your page, your server logs will show a visit. 123Stat correctly filters out all artificial traffic and only shows 'real' visitors.
Server log reports separate visitors by looking at their IPs ; more and more with cable modems, people use firewalls that change their IP at each HTTP request, so everytime one of these visitors requests a document from your site, the server logs will see a different IP and count a new visit. 123Stat will correctly identify these requests as part as a single visit. This alone causes large discrepancies as the server logs show a lot more visitors than actually came to your site.
123Stat's data is not derived from your server logs and this makes it much more precise than stats that may be supplied by your host.