What were the circumstances behind the loss of the "True Cross?"

It is my understanding that there was a relic, used by the Crusaders, that was claimed to be the very Cross on which Jesus was crucified. I also understand that sometime around 1187, it was captured by Muslims, and subsequently burned. What is the history behind this relic, and if it was believed to be something as important as the true cross, what on earth possessed them to do something as crazy as risk it in battle?