Can someone explain to a complete football novice how a .500 team will become bowl eligible just by beating 1 ranked conference opponent? Is this part of a conference tournament or something?
6 wins, for all intents and purposes, gets a team to bowl eligibility. There are oodles of bowl games that are tied to certain conferences based on teams' records (6+ wins). To get an invite, most bowls require a minimum of 6 wins but would prefer 7. If a bowl game that is tied-in to a conference that can't produce enough bowl eligible teams (6+wins), then they have the right to "shop elsewhere" and invite another 6+ win team. It is possible that a 6-win team does NOT get invited to a bowl game (ex - Temple last year was 6-6 and did not go to a bowl). For the most part, bowls invite teams that meet the minimum 6 wins AND they feel confident will sell tickets. Temple's fanbase does not have a great reputation for traveling or selling tickets in its own stadium.
For UConn, playing a ranked conference opponent is just a happy circumstance for this Saturday. If we beat either Houston on Saturday or Temple next Saturday, that will get us to 6 wins and bowl eligible. The resume, much like basketball RPI/SOS, would be greatly improved as the final win would come against a very tough, ranked opponent.
Here's a catch - let's say UConn wins on Saturday and only draws 20K. A bowl committee might pass on UConn in favor of another school who they feel would sell more tickets at their game. That's why it is fairly important that the football game draws well this Saturday. While the Pinstripe Bowl at Yankee Stadium would certainly consider UConn (if their tie-ins aren't all met), a bowl located somewhere else might not and point to dismal attendance at our last 2 home games against quality opponents as a reason why.
One more catch - it is possible that a 5-7 team could receive a bowl invite. But, again, the determining factors used for that would hurt UConn's chances. I think the tie breaking determination for 5-7 team invites is APR...and our football program scores 960, which is below other teams who would potentially be 5-7 (there is a posting on the football board of possible 5-7 teams APR scores if you are interested).
So to summarize this long-winded reply, our best chance at a bowl game is winning both games to close the year. Our next best chance is to win one of our final games...with a decent crowd in our last home game. Right now, the Courant is reporting that only 23K tickets have been sold for the game. That is incredibly and embarrassingly low for such a big game against a highly ranked opponent.
Hope this answers your question.