Playoffs or League Championship have two series of knockout baseball to determine who "wins the pennant" (by tradition, the league winners are given a pennant to fly over their stadium).
The first round is known as the "Divisional Series", it is played over the best-of-five games (the first two at one venue, then two at the other, then a fifth at the first venue if required), with the higher ranked team having "home field advantage" (i.e. three home games and two on the road).
The second round of the playoffs is known as the "Championship Series"; this one is played over the best-of-seven games, with home field advantage which means four home games (two games at one venue, three at the other, then two more at the first venue).
In the first round, the No.1 ranked team will play against the No.4 ranked team (and No.2 plays against the No.3), unless they came from the same division, in which event 1 plays 3, and 2 plays 4. Ties in the rankings are broken by the toss of a coin.
The League Championship Series started in 1969 as a five-game series, and in 1985 it was expanded to a seven-game format.
Just recently, ESPN reported that Major League Baseball filed a motion to move Alex Rodriguez's lawsuit against the league and commissioner Bud Selig to a federal court with the hope that a judge will eventually decide to dismiss the case, they believe that a federal judge would rule that Rodriguez is bound by the collective bargaining agreement to pursue his appeal through the arbitration process. Find out more at ESPN.