Emma and her brother were abducted and brainwashed, so as to forget their previous lives. They are being raised "safely" by members of the Others who desperately want their own children but are unable to conceive them.
I think that Cindy may be their real mother. It was never stated that she wasnt. And if they had never met their real mother then the wouldnt know what she looked like. And they newspaper said that the kids parents died in the plane crash.