Back in the olden days, the National League and American League would simply send their pennant winners to face each other in the World Series. As expansion expanded the leagues, that eventually carved out the opportunity for League Championship Series to serve as the opening act, allowing more teams to begin to claim ‘postseason appearances’ as a thing that actually had any sort of meaning.
By the time the 1994 strike rolled around and the further expansion brought in Florida and Colorado, MLB opted to carve out additional divisions - three each in the NL and AL - and Wild Card teams to round out a full quarterfinal-start to the baseball postseason.