This is important.
By missing out on a playoff team, the Big 12 lost out on about $6m, or about $400k per school after the participating team and the conference get their cut. That's not a small loss. $400k is enough to almost entirely fund a smaller program in the athletic department (tennis, golf, etc.).
This is almost entirely related to the teams being TCU and Baylor. If OU were involved, they would have gotten in. There's no way Ohio State would have leapfrogged a one loss Oklahoma. But the committee choosing between TCU, Ohio State or Baylor went with the brand name.
The Big 12 has to make a statement in the bowl games. TCU gets Ole Miss, an SEC team. TCU needs to put about 60 points on the board. Don't keep it close. Don't leave any doubt. Run it up as far as you can against the mighty SEC.
Baylor gets Michigan State. Oregon beat Michigan State by 19. That means Baylor needs to beat them by at least 24 to make sure everybody knows that they are a strong team.
West Virginia gets former Big 12 member (and current SEC member) A&M. WVU needs to get a win here. They don't have to score a million points, but they need to beat A&M.
Texas gets Arkansas and Texas absolutely must win. Other than TCU and Baylor, this is the matchup that the Big 12 most needs to do well in. Arkansas is a weaker SEC program. If Texas doesn't beat them (because Texas is a name program even though they are probably the 6th or 7th best team in the Big 12) the Big 12 looks bad. Horns must get the job done.
K-State faces UCLA again. This matchup is a very good matchup for the Cats. UCLA can't overwhelm them with talent, so they should be able to hang in and squeak out the W.
Oklahoma vs. Clemson, OU has to show up. Much like Texas, OU is the name school in football, so the Sooners have to demonstrate that they can take down a team from a weaker conference (ACC).
Oklahoma State and Washington's get together is a matchup of two teams with disappointing seasons. It'd be nice for OSU to win.
Heck, it would be great if the Big 12 went 7-0, but I doubt everybody wins. As long as TCU, Baylor, Texas and Oklahoma win, it can be considered a pretty solid bowl season. Either K-State or West Virginia notching a win would do wonders for the national perception. The most important thing (besides getting 4 or 5 wins) is to make sure that nobody gets blown out. And hope that the Big 10 does a collective thud in the bowls - Baylor can help that by destroying Michigan State.