Honestly, I think they're just curious. When people ask me about this process, they're always interested in which schools I applied to. Granted, it may have SOME bearing on your chances (depending on the opinions of the interviewer), but overall, I really think they just want to ask to see if anything really sticks out (like applying to 1 school or 30+ schools).
At a few interviews, they've asked me "How many," and one interviewer asked me specifically which schools I applied to. I just tell them honestly but don't reveal more information than what they're actually asking for. If they only want to know the number, I don't rattle off the names.