"Fit". That term can be the bane of existence for those applying for faculty jobs (like the one Dr. Becca just got, go congratulate her!). It can mean everything and nothing at the same time, but is intangible. If I had to write a definition it would be something along the lines of "the feel a department gets from you as to whether they want to deal with you everyday for the next 20 years."
Having been through a couple of searches on this side of the fence now, I can tell you that it is a major component of the search. As frustrating as it is to define, there is no question that you can sit through an interview with someone and be impressed by them, but have no interest in hiring them. It's kinda like test driving a car, sometimes they just don't feel right, even if you like all the features.
What is a candidate supposed to do to improve their chances on this front? Unfortunately, nothing. All you can do is be yourself* and hope that is what the department is looking for. I have been on both sides of a "fit" decision, so the reaction of one department to you could be completely different than another and it is entirely out of your control. In some respects there is a component of luck involved, realizing also that there are certain things that will turn your interviewers off entirely, no matter what they think of your work.
So, for those of you starting to hear back after interviews and getting bad news, don't get too frustrated. Realize that you may be an excellent candidate but just not be right for that particular department. Use the experience to refine your next interview and continue to build your CV for the next open spot that is perfect for you. With the benefit of a little time and space you may even realize that the position you land is a better fit for YOU than previous ones you interviewed for. I know I did.
*Assuming no one has ever described you as "axe-murderer-chic".