While not in the constitution itself, one of the writers of the document, Thomas Jefferson, wrote as an explanation of his intent:

"I contemplate with solemn reverence that act of the whole American people which declared that their legislature should "make no law respecting an establishment of religion, or prohibiting the free exercise thereof," thus building a wall of separation between Church and State."

The intent of the law was to protect religions from becoming a national religion, like the Church of England, and to prevent persecution for observing a different religion.

That being said, I don't really have a problem with not playing religious Christmas carols at the concert. If I want to hear religious music, I'll go to church. Both my sons were in our high school's music program and when it came to their holiday concerts they would play songs like "Winter Wonderland" and "Let it Snow". Occasionally they would play a religious song, but the director explained that, for the most part, Christmas carols are very simple songs and not very challenging to play. Since music is an academic class, the music they chose to play was a lot more complex and challenging.