It was actually the cloth that covered Jesus’ face:
Then Simon Peter came … and went into the tomb. He saw the linen cloths lying there, and the face cloth, which had been on Jesus’ head, not lying with the linen cloths but folded up in a place by itself.
The significance of the face cloth being folded is that it demonstrated that Jesus’ must have been alive. Anyone who had removed the body would not have bothered to unwrap it before carrying it off. Even if they had, they would not have bothered to fold the wrappings in an orderly fashion. So this small detail provides evidence that Jesus really had risen from the dead. When the disciples saw the grave clothes arranged in this way, they immediately understood the significance of it (John 20:8).