I have a woman working for me. She has a social security card. She says she is not "Legal". What constitutes "Legal"? Wouldn't she be considered a legal immigrant if she has a social security card? Is there other paperwork I need to look for?

Having SSN doesn't mean that person is "legal". Ask for copy of green card. You need both green card and SSN to verify legal status.

You should check with immigration, please read: USCIS - E-Verify