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?
About "doing crazy thing as risking in battle" - do you think Israelites were crazy for risking the Ark of the Covenant in battle?
About the history of finding of the Precious and Livegiving Cross - look here for the narration about Saint Helen http://www.goarch.org/special/listen_learn_share/exaltholycross
What is the history behind this relic?
There are legends about its pre-crucifixion origins
First off, there are legends about the origin of the cross before Jesus was crucified on it, such as it being made out of wood from the Garden of Eden. Several of these legends were included in the "13th Century bestseller" Golden Legends.
St. Helena, mother of Emperor Constantine, is said to have found it
The earliest account of the finding after the crucifixion is from Socrates Scholasticus (born c. 380) in his Ecclesiastical History. It was repeated by several other historians in the decades following, and Theodoret has a fairly concise version of it.
When the empress [St. Helena] beheld the place where the Saviour suffered, she immediately ordered the idolatrous temple, which had been there erected, to be destroyed, and the very earth on which it stood to be removed. When the tomb, which had been so long concealed, was discovered, three crosses were seen buried near the Lord's sepulchre. All held it as certain that one of these crosses was that of our Lord Jesus Christ, and that the other two were those of the thieves who were crucified with Him. Yet they could not discern to which of the three the Body of the Lord had been brought nigh, and which had received the outpouring of His precious Blood. But the wise and holy Macarius, the president of the city, resolved this question in the following manner. He caused a lady of rank, who had been long suffering from disease, to be touched by each of the crosses, with earnest prayer, and thus discerned the virtue residing in that of the Saviour. For the instant this cross was brought near the lady, it expelled the sore disease, and made her whole.
After the recovery
The Church of the Holy Sepulchre was built on the site of the crucifixion and burial of Jesus, and the relic was stored there for the benefit of worshippers. A nun named Egeria visited it in the 380s and described it as such:
Now, when it has been put upon the table, the bishop, as he sits, holds the extremities of the sacred wood firmly in his hands, while the deacons who stand around guard it. It is guarded thus because the custom is that the people, both faithful and catechumens, come one by one and, bowing down at the table, kiss the sacred wood and pass through. And because, I know not when, some one is said to have bitten off and stolen a portion of the sacred wood, it is thus guarded by the deacons who stand around, lest any one approaching should venture to do so again. And as all the people pass by one by one, all bowing themselves, they touch the Cross and the title, first with their foreheads and then with their eyes; then they kiss the Cross and pass through, but none lays his hand upon it to touch it.
In 614, the Sassanid Emperor Khosrau II ("Chosroes") captured the city of Jerusalem and removed the relic. In 628, the Byzantine Emperor Heraclius defeated Khosrau and returned the relic to Jerusalem two years later. The relic remained sealed, but at least one scholar suggests that the wood returned was a fake.
The Church of the Holy Sepulchre was destroyed around 1009 by Fatimid caliph Al-Hakim bi-Amr Allah. Christians hid the true cross until the city of Jerusalem was recaptured in the First Crusade. In the Third Crusade, Saladin during the Battle of Hattin in 1187 captured the True Cross, and attempts to ransom it back failed. The relic was not returned and it subsequently disappeared from historical records.
The relic today
The extant pieces of the True Cross are said to be fragments of the original that did not befall the same fate. It is common to divide relics into smaller pieces so that it can be seen more widely across the world. During the Fourth Crusade, Western Europeans who invaded Constantinople found two fo the largest pieces. A knight named Robert de Clari wrote:
Within this chapel were found many precious relics; for therein were found two pieces of the True Cross, as thick as a man's leg and a fathom in length.
Most pieces within Europe come from these two relics. There were also an extraordinary number of fakes produced, as commented on by John Calvin, who said that there were so many they could fill a boat.
There is no abbey so poor as not to have a specimen. In some places there are large fragments, as at the Holy Chapel in Paris, at Poitiers, and at Rome, where a good-sized crucifix is said to have been made of it. In brief, if all the pieces that could be found were collected together, they would make a big ship-load. Yet the Gospel testifies that a single man was able to carry it.
—Traité Des Reliques
That said, in 1870, Charles Rohault de Fleury took an inventory of all purported relics of the True Cross in his day and came to the conclusion that together, they would only have made up one third of the original cross.
There are a number of sites today where you can find the True Cross. One of the largest today can be found in the Monastery of Santo Toribio de Liébana in Spain. In North America, the Treasures of the Church traveling exhibition contains a piece of the True Cross as one of its relics.
Why risk the True Cross in battle?
As described above, there were times when Jerusalem was captured and the Ark had to be moved. And if it's on the move, why not take it somewhere where it will be useful? Most likely, the crusaders were motivated by the Old Testament descriptions of the Ark of the Covenant being used in battle against the Philistines.
When the soldiers returned to camp, the elders of Israel asked, “Why did the Lord bring defeat on us today before the Philistines? Let us bring the ark of the Lord’s covenant from Shiloh, so that he may go with us and save us from the hand of our enemies.”
So the people sent men to Shiloh, and they brought back the ark of the covenant of the Lord Almighty, who is enthroned between the cherubim. And Eli’s two sons, Hophni and Phinehas, were there with the ark of the covenant of God.
When the ark of the Lord’s covenant came into the camp, all Israel raised such a great shout that the ground shook. Hearing the uproar, the Philistines asked, “What’s all this shouting in the Hebrew camp?”
When they learned that the ark of the Lord had come into the camp, the Philistines were afraid. “A god has come into the camp,” they said. “Oh no! Nothing like this has happened before. We’re doomed! Who will deliver us from the hand of these mighty gods? They are the gods who struck the Egyptians with all kinds of plagues in the wilderness.
—1 Samuel 4:3-8 (NIV)
Unfortunately for the Israelites, the Ark was captured, but everywhere that it was taken, the Philistines suffered plagues and other maladies until the Philistines decided that they had had enough and returned it to the Israelites. Likely the crusaders hoped the same fate would befall the Muslims when Saladin captured it, but that did not occur.