Doubting Thomas is a derogatory term for a someone who refuses to believe without evidence.
The term refers to John 20:24-29 : after Jesus' resurrection, he appeared to his apostles, except for Thomas, who was not present. When the other apostles told him about it, he said he would not believe Jesus was resurrected unless he could put his finger in the nail holes and touch the spear wound in Jesus' side. A week later, Jesus returned and allowed Thomas to touch his wounds, at which point Thomas was convinced that Jesus had indeed returned. The story concludes with
29 Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed.
Thomas and skepticism
Thomas was presented with an extraordinary claim (that a man had come back from the dead), and refused to believe it on the say-so of his friends. Once he had been given extraordinary evidence, he changed his mind and accepted the claim. In other words, he acted like an honest skeptic, and was rebuked for it.