When I am the one being interviewed I often ask a few questions up front to qualify the situation. It give me a little info to tailor my talking points as well as immediately transforming it from an interview into a conversation.
A few questions I'll typically lead with:
1) have you had time to review my work before hand?
2) are there any projects you are particularly interested in getting the full back story on?
3) what about my work interested you?
4) what are you looking to augment or enhance with this open position?
A couple of those get the ball rolling. Making the session about finding a solution to their problem, which is needing to fill an open head count. Filling an open head count is a lot of work on the hiring side. First the person has likely done battle with those who control the budget to secure the funds to hire someone. That might have taken months. Then they had to work with HR to get a job req and job description approved and posted on a bunch of sites that HR probably did;t want to pay for. Then they had to sort through a couple hundred resumes, 90% of which had little to no relevance, get consensus on the final 3-5 they they were going to interview, and do all that while doing their actual job.... and now here they are in a room (or on Skype) with you.
Asking them what they want can be a nice way to acknowledge how much work they have put in to getting to meet you in that moment.