This question originally appeared on Quora. 
Answer by Riley Patterson, BCS Apologist
To understand the BCS, it's important to know about the system that preceded it.
College football's postseason began as one-off "bowl games." These were organized more or less independently by stadium owners and cities that wanted to host big events around New Year's. The bowl game organizers naturally sought out the best matchups, so the early bowls would often pit two conference champions against each other and have major effects on the subjective national polls that would crown a "national champion" at the end of the year. As the system grew and evolved, the more prestigious bowls drew up contracts with the power conferences to guarantee the conference champion's berth in that particular bowl. For decades, the Big 10 champion would unconditionally play the Pac 10 champion in the Rose Bowl, while the Southwest Conference always sent its champion to the Cotton Bowl and the Big 8 champion would play in the Orange Bowl. There were dozens more of these arrangements including other conference champions as well as #2 and #3 teams.
This was a great business arrangement for both conferences and bowl organizers, but you can see how it might lead to problems for those who operate under the assumption that the postseason exists to help crown a single national champion. It's not altogether unlikely that the top three teams in the national polls at the end of the regular season might be the champions of three different conferences already committed to three different bowls. In fact, a #1 vs. #2 matchup was by far the exception rather than the rule. As the coveted "national championship" title awarded to #1 in the AP and other polls became more important, fans, players, and coaches complained about the degree of subjectivity involved in selecting a #1 when the top four or five teams had never played each other.
The BCS, or Bowl Championship Series, proved to be the most successful of several attempts to fix some of the problems with the ad hoc bowl-conference pairings. The six strongest conferences all commit their champions to BCS controlled bowls, which also draw from some non-champions and exceptional teams outside of these six conferences. The important distinction is that the conference champions are not inflexibly tied to a single bowl game. Rather, the top two teams, as decided by the combination of a media poll, a coaches poll, and computer rankings, play each other head to head in a different location each year, presumably to objectively decide the national title on the field. When people speak of "winning the BCS," they refer to this #1 vs. #2 matchup, or the BCS National Championship Game. The only way to get there is by earning one of the top two rankings during the course of the regular season, which typically means going undefeated or sustaining only a single loss to a quality team, though there are exceptions. Once a team makes it to this game, they simply need to win on the field.
The BCS controls four bowl games as well as the national championship. The conference champions and a number of at-large teams that don't make it to the championship are matched up in these bowl games by way of a complicated system involving some of the old contractual tie-ins as well as a set of rules that might remind you of picking dodgeball teams in gym class. Only major advertising deals and millions of dollars are on the line.
To summarize, the BCS is best understood as a compromise between several prestigious bowl games and conferences to allow for slightly more objectivity in how college football decides its champion. This agreement is constructed as centralized long-term organization rotating the national championship game between the four associated bowls so that they can all be comfortable with the deal. The complicated rotation is necessary because each bowl organizing committee refuses to give up their traditional right to a potentially #1 or #2 team without getting something in return.
In recent years, there have been even more complaints about the subjectivity inherent in selecting college football's champion, notably around how #1 and #2 are decided and the fact that #3 never gets a shot to prove itself. Just recently, an agreement was made to tweak the system to enter the four top-ranked teams into a playoff in order to assuage some of these concerns. Whether this will lead to reliable, objective consensus on college football's champion remains to be seen. Don't hold your breath.