Shroud of Turin
The Shroud of Turin is a piece of linen cloth bearing what could be the image of a man who suffered physical trauma. Many people associate this image with Jesus.
The Shroud in Assassin's Creed
In the Assassin's Creed universe, "The Shroud" refers to one of the Pieces of Eden, more specifically PE66. It is believed that, like most of the Pieces of Eden, several historical figures throughout a wide span of eras got their hands on The Shroud. Examples include David, Jason, Joseph and Jesus.
Its uses remain unknown, though most of the allusions in the game point in the direction of healing, curing ailments and even resurrecting the dead. This theory is reinforced by the story in the Bible about an ill woman that touched Jesus' robes whose health was reverted back to normal.