The RPI referred to in the more recent assessments of NCAA regional matchups is the pseudo Ratings Power Index developed by Boyd Nation in an attempt to simulate the actual RPI used by the NCAA to rank baseball teams and conferences. Boyd has also developed his own ranking system, the ISR.
You can find the full collection of ISRs and pseudo-RPIs linked from Boyd's College Baseball Ratings Page. For a direct link to the pRPI, click here.
For your convenience, I'll summarize some key features of the RPI here. If you want more detail, you should read the FAQ Boyd wrote that answers many common questions about the different ratings. Note that Boyd obtained more information about the NCAA system between the 1999 and 2000 season, so the pRPI before 2000 is different in detail from the one generated now.
The RPI is an index developed by the NCAA to help select and seed teams for NCAA tournaments. The key word here is help, since the committee can and does use other information, but the RPI is a key piece of the puzzle as you can see from looking at tournament bids. Note that my tables use the ranking rather than the raw RPI value, and that a tiny (1 part in 10,000) change in an RPI value (such as will result from the corrections the NCAA applies) can sometimes change the ranking by several places for mid-pack teams. If you want the actual values for the pRPIs, you should consult Boyd's tables for a given season.
The pseudo-RPI tabulated in 1998 and 1999 was the result of employing a best guess at the basic part of the NCAA formula. Boyd used 0.3 * WP + 0.4 * OWP + 0.3 * OOWP, where WP is the team's winning percentage, OWP is their opponents' winning percentage with games against the team in question removed, and OOWP is their opponents' opponents' winning percentages.
Boyd notes that the official formula also includes adjustments for too many games against non-Division I teams, important road wins, and home losses to lesser teams. For 2000 and beyond, Boyd will use a good estimate of how these additional corrections are done. See his web site for details.