The first amendment basics
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
In basic terms this is the right to express yourself freely through speech,press,assemble together and petition against the government freely and peacefully.
Supreme court case over the amendment
The officials were going to court over a holiday display dispute on public property. The argument was over a menorah or a creche. They were fighting over the constitutionality of the displays and it was later brought to the Supreme Court of Justice.
The court's decision was in favor of the menorah. The menorah was ruled as constitutional. Rather than the creche which was unconstitutional violating the Establishment Clause. 6-3 of the justices voted for the creche to be unconstitutional.
Citation 1:SCHLAG, PIERRE. "First Amendment (Update 1)." Encyclopedia of the American Constitution. Ed. Leonard W. Levy and Kenneth L. Karst. 2nd ed. Vol. 3. Detroit: Macmillan Reference USA, 2000. 1053-1055. Gale Virtual Reference Library. Web. 7 Dec. 2015.