The Scopes Trial became the “trial of the century” (in some people’s minds, at least), because it tapped in to some of the biggest trends and issues of the day. In addition, it became the trial of the century because it came about at a time when radio was starting to boom. These two factors combined to make this a very high-profile trial indeed.
Before the 1920s, it would have been very difficult for any trial to capture the attention of the whole country. There was simply no way of immediately communicating things about the trial to many people far away. There was certainly no way that people far away could actually hear the events of the trial live. By 1925, however, this had changed. Radios were now common, which meant that the Scopes Trial could become the first trial ever to be broadcast live. This helped greatly in bringing attention to the trial, allowing it to become the trial of the century.
Of course, in order for it to be the trial of the century, it also had to be interesting to a large number of people. The Scopes Trial was interesting to many people because it was connected to major issues of the time. During the 1920s, American culture was changing. Particularly in the cities, the old values were disappearing and being replaced with new ones. This was a time of jazz and flappers and illicit drinking. It was a time when more people were moving to cities and leaving fewer in rural areas. In other words, the old, rural, America with its traditional values was starting to be replaced by a newer, more urban society with newer values. This made for a great deal of conflict between people who liked the old society and those in favor of the new (this is not unlike the way things are today).
The Scopes Trial became famous because it pitted these two sides against one another. The new society believed in things like evolution while the old believed in old-fashioned religion. The new society was typified by people like H. L. Mencken, who covered the trial and looked down on the hicks of Dayton, TN while the old society was championed by traditionalists like William Jennings Bryan (who prosecuted the case). It was presented as a war between new and old America. Bryan argued that “if evolution wins, Christianity goes” while Clarence Darrow (defending Scopes) claimed that “Scopes isn't on trial; civilization is on trial” and said that the prosecution was trying to bring America back to the Dark Ages.
In short, this trial became a huge deal because it could be broadcast across the country and because it could be presented as a struggle between two contending visions of what the US should be.