I interned for a small advertising agency in a smallish city in Missouri. Internships are really all over the board and can consist of pretty much anything the agency wants them to be.
For me, I spent probably 15 hours per week there, and only my billable hours were paid, and at a very low rate. My work consisted mainly of comps which the main designer (singular...very small firm) would use to create the finished product. I think that I personally got to actually design 2-3 pieces over the semester that were produced the way I designed them.
I also went on a couple of photoshoots and watched how that process goes.
I'd say mine was a decent experience, and helped me get familiar with the day-to-day job of designing.
But really, ATD, it can be anything you want it to be...or anything you and your protegé decide on. Keep in mind that some of the time you spend productively now will be spent helping the intern get adjusted to his or her surroundings answering questions that you know the answer to because you've used the printer before, you know the filing system that you've created...as well as technical questions that the intern doesn't know simply because of lack of experience.
I honestly wouldn't expect to be able to take on all that much more work, especially at first, and maybe not more than one or two pieces over the course of the internship. However, I think the experience will be most valuable as a way to give back to the design community, and as a way to learn more about yourself in the process.
Good luck, and, judging by your portfolio, your intern will learn a ton about great design!