Typically this phrase is used in a midly derogatory. It describes someone who refuse to simply believe in something out of pure faith without asking for evidence. A devout Christian might consider me to be a doubting thomas because I don't believe there is a God since there's no evidence. The Christian considers it a bad thing that I'm not simply willing to have some faith.
Athiest: Normal people don't consider it a bad thing when others ask for proof when they make extraordinary claims. If I said that I am Zrlak, King of Mars, I would have little respect for you if you believed me without asking for evidence yet you expect me to just believe your equally ridiculous claims?