The Scopes Trial is relevant today in the United States because many of the same issues raised in that trial continue to be controversial today. This was a trial that brought up issues of science and religious faith, issues that still exist today.
The Scopes Trial came about because the state of Tennessee had a law that banned the teaching of evolution in the public schools. Teaching evolution was banned because Christians in the state felt that it was contrary to their faith. This was a major issue in those days because Christians felt that their faith was under attack from new ideas. They were trying to fight back against what they saw as excessive secularism. Today, Christians feel this same way, perhaps to an even greater degree. Christians feel that US society has tried to push faith out of the public arena. They are angry about things like (in their minds) the war on Christmas and the move towards legalized gay marriage. There are still places where there is controversy over the teaching of evolution and many Christians do not believe in that scientific theory.
In this way, the issues that were presented by the Scopes Trial continue to be relevant today.