From Wikipedia:
The World Series is the annual championship series of Major League Baseball, played between the American League and National League champions since 1903. The winner of the World Series championship is determined through a best-of-seven playoff and awarded the Commissioner's Trophy. Because the World Series is played in October, it is sometimes called the Fall Classic.
Until the formation of the American Association in 1882 as a second major league, the National Association of Professional Base Ball Players (1871–75) and then the National League (founded 1876) represented the top level of organized baseball in the United States. All championships went to whoever had the best record at the end of the season, without a postseason series being played. Starting in 1884 and going through 1890, the National League and the American Association faced each other in a series of games at the end of the season to determine an overall champion. These matchups were disorganized in comparison to the modern Series: games played ranged from as few as three in 1884 to a high of 15 in 1887 (Detroit beat St. Louis 10 games to 5), and both the 1885 and 1890 Series ended in ties, each team having won three games with one tie game.
The series were promoted and referred to as "The Championship of the United States," "World's Championship Series," or "World's Series" for short.
The 19th-century competitions are, however, not officially recognized as part of World Series history by Major League Baseball, as the organization considers 19th-century baseball to be a prologue to the modern baseball era. Until about 1960, some sources treated the 19th-century Series on an equal basis with the post-19th-century series. After about 1930, however, many authorities list the start of the World Series in 1903 and discuss the earlier contests separately. (For example, the 1929 World Almanac and Book of Facts lists "Baseball's World Championships 1884–1928" in a single table, but the 1943 edition lists "Baseball World Championships–1903-1942".