it's a person who does not believe whatever you tell them. They will always seek proof and evidence.
It comes from the bible where St Thomas refused to believe christ (jesus) was dead, had been crucified, until he had received proof of it.
EDIT: I am not religious I made a small mistake, Thomas did not believe Christ had risen. He refused to believe it until he could fell and touch Jesus' wounds himself.
A doubting Thomas could also be someone who is habitually pessimistic.