This is a baseball term which refers to the extremely rare fear of a pitcher throwing only nine pitches, all strikes, and getting three outs, in a given half inning. It has only been done 46 times by 43 pitchers in the history of Major League Baseball. As one might imagine, throwing nine strikes in a row is hard enough; getting the players out in the process make it infinitely harder. The three Major League pitchers who have accomplished this feat twice are: Lefty Grove, Sandy Koufax, and Nolan Ryan. All three are Hall-of Fame Players, as are nine other pitchers who have done it. The most recent occurance of an immaculate inning was Juan Perez on July 8th, 2011.
The phrase comes from the notion that a nine pitch, three strike inning is a perfect representation of how a pitcher should perform. However, since the adjective, "perfect," applies to a different concept in baseball, the synonym, "immaculate" caught on and has stuck. In baseball, a perfect game or inning involves no hitters getting on base. This is not an official statistic, but can be easily tracked since pitch counts and the data necessary is now electronic.