What is it?
The Shroud of Turin is an approximately 14 ft. by 3.5 ft. piece of woven linen. It shows faint images of the front and back of a bearded man joined at the head, as though it had been folded from his feet, over his head, and back to his feet. There are also red blotches at the locations of Christ's stigmata: around the head, on the wrists and feet, and on the side of the body. It is believed by many to be the burial shroud of Jesus of Nazareth, and those who believe in its origins consider it a profound religious artifact. There have been numerous studies claiming to both prove and debunk the possibility that it is spatially and temporally contemporary to the life of Jesus.
It first showed up at the St. Mary of Lirey church in Lirey, France, built by Geoffrey de Charny around 1350 AD. De Charny was already in possession of the Shroud when he wrote Pope Clement VI about his intention to build the church, but the first exposition of the Shroud wasn't until about 1355. That first exposition attracted many pilgrims, and also the attention of local Bishop Henri, who didn't believe in its origin and demanded the exposition shut down. It moved from possession by the de Charny to the Savoy family and was shown here and there around Europe. It was housed permanently in Turin in 1578, and turned over to the Catholic church in 1988.
During its travels through Europe the shroud suffered quite a bit of abuse. In 1532 a fire broke out in the chapel that held the shroud, and since it was locked up a blacksmith had to be called to rescue it. In the end the shroud was scorched badly and a single hole was burnt through it by a drop of molten silver. A Savoy courtier had earlier noted that the shroud had been tried by fire, laundered many times, and even boiled in oil, but it must have been a genuine artifact because "... it was not possible to efface or remove the imprint and image."
When was it made?
In 1988 the Vatican allowed fragments of the shroud to be C-14 radiocarbon dated by three laboratories: Oxford University, the University of Arizona, and the Swiss Federal Institute of Technology. Each laboratory used strict scientific rigor in their analysis, and they all came up with a date of around 1350 AD. This was basically in line with earlier radiocarbon dating that had placed the linen as being harvested in 1325, and microscopy by the same team that put the date at 1350. With almost perfect certainty, the linen was harvested, woven, and turned into art sometime during the fourteenth century.
Some have argued that the C-14 dating was contaminated by the 1532 fire. Their theory goes that the shroud was enriched with C-14 (and its much more common non-radioactive cousin C-12) because of the carbon dioxide rich atmosphere during the fire. Radiocarbon dating is done by measuring how much less C-14 is in the sample than in regular biomass, so enriched C-14 would've made the samples seem newer. Studies done in Russia and at the University of Arizona both suggest that any C-14 enrichment would've been short lived and small, and thus wouldn't have changed the calculated date.
Another theory to explain away the radiocarbon dating results is that the process may have been thrown off by all bacteria and fungi that have lived on the Shroud's fibers since it was made. Referred to as a "bioplastic coating," this residue has been building up since the linen was made, and thus has recent and ancient carbon content. Unfortunately for that theory C-14 decays at a logarithmic rate rather than at a linear (or flat!) one. Thus, by one graph I looked at, there would need to be almost twice as many modern carbon atoms as there are original ones to throw the date 1300 years into the future. Since the 20 pound shroud obviously doesn't have another 40 pounds of biomass hanging off of it, this theory is almost surely false.
Who is on it?
Jesus of Nazareth, that one was easy. A quite common Medieval representation of Jesus, with his arms crossed as they were described in the bible. The portrait is between five feet ten inches and six feet tall, not known for sure because the linen has shrunk and stretched in different places. The arms and fingers are abnormally long and thin, the left arm is longer than the right, and the head is elongated and about 5% larger than would be proportionate to the body. Some shroud believers argue that this body shape is the result of Marfan Syndrome, which coincidentally is thought to be responsible for Abraham Lincoln's odd stature. In fact, the image conforms to Medieval artistic standards -- long fingers and an elongated head were simply the accepted style for representing the human body at the time.
How was it made?
For a long while it was assumed that the image was painted, but because there weren't any visible brush strokes and the image didn't go very deep into the linen this was widely challenged. It was also proposed that the image came from draping the shroud over an actual person or body and doing a rubbing, or even by a process where pigment is made to evaporate off a person and be absorbed by the surrounding cloth. Since the image isn't proportioned right to have been made by a three dimensional body, this theory is also hard to believe.
As it turns out, the image was made by rubbing, but from a bas-relief pressed metal plate rather than an actual person. The artist probably used an already-existing pressed or hammered brass bas-relief of Jesus, and lightly dabbed on tempera paint to make the image. This method accounts for the faux-three-dimensional proportioning of the image, as well as its shallow depth. Since Medieval and Renaissance works of art featuring the Shroud show its image quite clearly, the tempera must have been very visible in the past. Due to the constant laundering and boiling the pigment eventually wore off, leaving only the ghostly negative image (likely due to chemical changes done to the linen by the tempera binder) present today.
Chemical analyses have picked up traces of iron oxide (red ochre) and mercuric sulfide (vermilion) in the image and blood areas of the Shroud, from pigments used in the tempera. Blood areas were also dabbed on, probably while the linen was still stretched over the bas-relief used for the rest of the image. We know that the blood areas are not actually blood because they fail forensic tests for blood, except for a very basic test that only looks for iron oxide and protein, both supplied by the tempera. Also, blood turns brown-black when it dries, not the very red vermilion found on the shroud.
One of the most unlikely theories, but worth mentioning because it is so bizarre, is that the shroud was made by a very primitive form of photography. I found a whole web page dedicated to the subject, including the chemical components needed for exposure and design of the building that would need to act as a camera obscura for the technique to work. Notably, the process would have required a developer made mostly of urine and a window-sized convex lens of ground quartz.
Where was it made?
Since de Charny was in possession of the shroud in 1350, most believe that he brought it back from Constantinople some time during the Crusades. Adding to this theory is the presence of pollen on the Shroud that is only found in that area, though it has been suggested that the pollen is a hoax perpetrated by a die-hard Shroud believer. It should also be noted that the face on the Shroud is much like the Byzantine portraits of Jesus that are extant today, further pointing to origination in the area that is now Turkey.