What is the significance of the Appomattox court house?

I assume you mean Appomattox Court House in Appomattox, VA, where Gen. Robert E. Lee finally surrendered to Union Army Gen. Ulysses S. Grant. This event, which took place on April 9, 1865, essentially marked the end of the U.S. Civil War, a conflict between the slave-owning South, which had become a Confederacy and seceded from the nation, and the Union in the North.
The U.S. Civil War lasted from 1861 to 1865 and was the deadliest war America ever fought. More Americans died in this conflict than in World War I and World War II combined. It shaped American History for years to come and is one of the country's defining events.
Lee's surrender at Appomattox followed on the heels of a last ditch battle that same morning—the Battle of Appomattox Courthouse. Lee was trying to move what was left of his army south to rejoin Confederate forces in North Carolina. His force was intercepted by the Union Army and almost destroyed. As such, he had no choice but to surrender. The Confederacy was already in dire straits by this point. Gen. Sherman had already gone on his famous march to Atlanta, destroying the southern railroads and burning towns and other infrastructure. There was little left of southern resistance by the spring of 1865.