The asterisk was made famous in 1961 by Commissioner Ford Frick. Frick, a friend of Babe Ruth was upset that Roger Maris would be breaking Ruth's single season home run record in the first year of the 162 game schedule.
As a result, Frick ruled that Ruth's record would be listed with an asterisk calling attention to a footnote that stated that Ruth's record was achieved in a 154 game season and Maris's mark happened in a 162 game season.
Contrary to popular belief, Ruth's record did not stand after 1961. It was merely placed in the record books with a footnote in deference to the legend. The point was made moot in 1998, when Mark McGwire and Sammy Sosa both hit 61 home runs in fewer than 154 games.
The asterisk can be seen in the title of the HBO movie 61*.