Here's a great example of a question that is designed to be a conversation-starter about how you would be a great fit for the company. Before you ask this question, it's important that you've done your homework about the company. You should feel confident that your skills and experience are good matches with open positions at the company. This is not the time, however, to try to jam a square peg into a round hole. Recruiters will see through that immediately.
After asking about the desirable skills and attributes, pay close attention to what the recruiter actually says. Choose a few specific characteristics and try to tie them to specific examples from your professional or educational life -- internships, project leadership, daily responsibilities -- that show why you're the right person for the job. Share one or two of those experiences with the recruiter and point out the related entries on your résumé.