The purpose of the Log Browser is twofold. The obvious one is to give an example of how to use mod_sqil and Cindy.pm. Logging with mod_log_sql is simply the easiest way to get a database with a reasonable amount of data. The Log Browser also demonstrates that you can get quite far with a pure REST approach without any server side state. The server only does data transformations. All view state is in the URLs.
The architecture has two layers. The database layer is handled by mod_sqil, which does database queries that return their results as xml. The presentation layer is handled by Cindy, which uses XPath to grab data from the database layer and move them into an HTML template.
If you take a closer look at log.sqil, you will see that the same WHERE conditions are repeated several times. An include will be added to fix this. Looking inside the navigation tag you will also see, that for the more complex features the SQL has to be quite smart.