The simple answer is drama. Dramas require storylines. Coverage of the NFL has done a great job of creating storylines that make games interesting for casual fans. College football has the advantage that the actors change every couple of years making the creation of new storylines even easier.
However, those storylines are empty without one key component: pressure. Without the pressure to reach the top riding on their actions, no one cares about the actors. If a mayor in a town of 1000 has an extra-marital affair with an intern, no one cares outside the town. If the President of the United States does, it is of huge interest across the country.
The college football product as it relates to expanding interest from casual fans suffers from lack of pressure making their storylines bland and uninteresting. None of the bowl games mean anything. So you win or lose the Rose/Cotton/Earl Schieb Paint the Toilet Bowl. So what? If there is no meaning in the outcome, there is no perceived pressure in victory and the drama falls flat.
What about the championship game itself? Given the above description, it should have all the elements necessary. It does but to a substantially lesser degree because no fan perceives the game as actually crowning a champion. If the audience does not believe the outcome to truly determine the champion, then perceived pressure no longer exists, the drama disappears and the casual fans lose interest. I'm sure the Florida and Oklahoma fans cared about the outcome, but how many people that were not fans of either school cared?
A playoff makes seven to fifteen games have meaning instead of just one and that pressure builds with each successive win. The "you came all this way" storyline emerges. In addition, it opens new potential storylines such as upsets. In the current format, it is simply not possible for a Cinderella team to "upset" the BCS because an army of voters must consider the Cinderella worthy of playing for the championship which by definition means they are no longer a Cinderella team. There are other storylines that are excluded by the current system such as the team that overcomes early adversity to win it all.
The list of storylines that might be possible in a playoff far outweighs those in the current system and that translates to greater interest from casual fans and that translates into more money.