Women don't fit in binders.
I mean, seriously. If he had said "binders full of RESUMES" there wouldn't be a meme. "Binders full of women" reduces women to what they can fit on an 8.5 by 11 sheet of paper with three holes in it. People aren't their CVs -- only employers, very WEALTHY employers who don't interact with most of their staff, think of them that way.
For the record, it would've been just as bad to say "binders full of people," but the way he said it fit with the narrative of his answer as being basically inhospitable to women in the workforce, since his solution to fair pay is "I pay women fairly!" rather than, say, how he might ensure others do so. A consistent theme of Mitt's responses to problems is that, instead of explaining how society might solve it, he explains how HE had solved it previously with his millions of dollars -- this is the same thing that happened with Paul Ryan's line about the car accident and Mitt paying for that guy's bills. If Mitt's proposing to hire every woman in America, then his willingness to pay them fairly resolves the problem, but if not then he needs an actual policy solution.