There are two major reasons for this.

First, the trial featured nationally known lawyers/public figures on each side.  William Jennings Bryan had run for president a number of times.  Clarence Darrow was perhaps the most famous attorney in the country.  Their high profile helped to attract attention to the case.

Second, the case had to do with issues that were very important in the country at the time.  The 1920s was a decade of major social change.  Traditional values were in decline and new values were appearing.  The whole issue of evolution and fundamentalism was just an example of that general trend.  

This trial attracted attention because the issue played into this major tension between traditional values and new ways that was present in the 1920s.  This, combined with the fame of the lawyers involved, caused people to pay a great deal of attention to the trial.