Lucene (
http://lucene.apache.org/) is the indexing service. The admin screen with stats show the current state of the what has been indexed. The dates, etc in the admin screen are in reference to "re-indexing" the site with those criteria.
The 3 files you're asking about are the index files created by Lucene.
As to a reporting feature... there isn't one. Mostly because people want different things reported in different formats and it's fairly easy to get the basic stuff out of the databases with queries. E.g., to get a count of posts per forum:
So most people "roll their own" reports.
[originally posted on jforum.net by monroe]