It's a bit convoluted. It wasn't a symbol of the Klan initially. However, in the 1915 movie Birth of a Nation, the Klan burns a cross as a way to rally members. If you don't know this film, it's a very hateful movie about the founding of the Klan--not accurate, but kind of a mythmaking enterprise that was one of the most successful and influential films ever made.

There have really been 3 Klans. There was the terrorist militia that was founded after the Civil War. But that kind of petered out. Then, when Birth of a Nation came out, it inspired a whole rebirth of the Klan, and it became an extremely widespread and popular social organization. (Klan #3 was what arose in the wake of the civil rights movement). As this reborn group had been inspired by Birth of a Nation, they adopted some of the practices they saw in the film, including the cross burning. So, why was there a cross burning in the film if the original Klan hadn't done that?

That practice came from an unlikely source--the novels of Sir Walter Scott. He wrote these really romantic, chivalric novels that were highly popular and influential in the 19th century. His most famous one is Ivanhoe. He was particularly romantic and inspirational about the history of highland Scots. Don't underestimate his novels' importance--Mark Twain only slightly jokingly blamed the civil war on Sir Walter Scott, because he felt that Scott made these sorts of quixotic wars for honor into romantic tales that inspired people with feelings of glory, when in reality wars are bloody and dirty and horrible.

It was this sentiment that led Twain to write A Connecticut Yankee in King Arthur's Court. He was spoofing this kind of mythic tales of chivalry. His story ends up bloody and horrific. But even so, many people saw A Connecticut Yankee as a ripping yarn while missing Twain's message.

So anyway, in Scott's tales, the highland clans lit burning crosses on hills in order to rally them together. This in turn inspired D.W. Griffiths, the director of Birth of a Nation, to have burning crosses in the film on the part of the KKK--a really eye-catching and inspirational visual that tied the newly born Klan with the chivalric glory described by Sir Walter Scott, and celebrated the heritage of many of the KKK members.

Most Klan members and chapters insist that they don't "burn" crosses, but rather that they "light" them. From the research I've conducted (and honestly feel a little unclean after doing so!), it looks like the practice comes from two notions:

1. The medieval Scottish clan practice of lighting crosses upon hills to act as signals.

2. The lighting of the cross symbolizes that the light of Jesus is still present in today's society, and the Klan is trying to emphasize that it is trying to simply remind the world of Jesus' light amid the strife caused by those they feel are desecrating Jesus' ideals.

I took my information from sites such as The Aryan Nations Knights and Thomas Dixon's 1905 novel "The Clansman: An Historical Romance of the Ku Klux Klan", which included an illustration of the Scottish ritual.