Here's the skinny:
1) What does the number displayed in the Public Games window actually represent?
The number that displays in the Public Games window represents the total number of games currently available, based on your game region and mode (Hardcore heroes qualify for a different set of Public Games). The number does not represent private games or Public Games that already have four players. Players hanging out in the character menus or using the auction house are not considered here either.
2) Why did that number suddenly change so much after patch 1.0.3?
Prior to patch 1.0.3, the in-game matchmaking system would often create new Public Games instead of filling existing games to their maximum capacity of four players. That configuration was to help reduce server load within individual games (fewer players, less load); however, it caused situations where players were rarely being placed into full games, and our goal has always been to promote the four player cooperative experience in Diablo III.
In patch 1.0.3 we made some changes so that the matchmaking system would attempt to fill Public Games instead of creating new ones whenever possible. As a result, we're seeing more filled Public Games than ever before (you may have noticed this yourself while playing), but it also means that the number displayed in the Public Games window generally isn't as high as it was prior to patch 1.0.3. As explained above, this is due to the fact that the value only reflects Public Games which aren't yet full.
We understand that labeling this number as "In Games" in the Public Games window can be confusing, so we're currently looking into ways to make the number and what it represents more clear. In the meantime, we continue to closely monitor both the state of the game service and your questions and comments about Diablo III.