When professional baseball first organized itself in 1871, it was in the form of a single organization: The National Association of Professional Baseball Players. Any club claiming to be professional could join upon payment of modest dues. As a result, clubs varied enormously in strength, with some being little more than semi-pro groups who had no financial backers. This led to a huge disparity in strength: One club would go 71-8; while another was going 2-46 while sharing in the gate receipts of the stronger clubs!

There were other problems: Fan rowdiness and gamblers led to game-fixing, and drove away families and middle-class fans. Clubs stole players under contract to others, and protected them from lawsuits. Clubs sometimes cancelled road trips if they thought they'd lose money.The player-controlled Association did nothing about these problems.

The National League was formed in 1876 to address all these problems. Clubs had to have strong financial backing to join the NL, and were assigned exclusive urban territories. Owners and the NL President took administrative control from the players, and clubs and players were expelled for abuses. (The NYC club was thrown out of the NL for cancelling road trips, I believe).
Steps were taken to discourage rowdy fans, such as increasing admission fees and banning alcohol.

With the concept of a Major League" thus established by the NL, baseball took on a broader fan appeal that took it out of its "low-class" social status. The exclusivity of the NL led to the creation of minor leagues. Later, other major leagues were tried, but all failed until the creation of the AL in 1901.

Through all this, the Boston club ( now Atlanta Braves) survived without interruption fromn 1871 until now. The Chicago club (today's Cubs) also survived from 1871, except for a two-year lapse after the Chicago fire.