The ladies above provided really good answers and examples. As much as this may sounds weird I like to define it as simple feeling a "click" or "connection" with the parents. You have to feel comfortable with them and them with you, however in a professional not chummy way. They have to show respect in your home and while discussing potential care and you have to seem to be on the same page when it comes to general thoughts regarding child rearing and overall values. It is very important for you and them to realize that the interview is going both ways: as much as they want a good provider, you want a good family and fit. I strongly believe that you have to follow your gut because you can't always rationale a feeling, but very seldom is a gut feeling wrong!