Are you trying to develop a writing voice? Want to get better at interviewing other people? Don't know the first thing about how social media works? These are all things you can learn more about from the professionals. The thing is, you're literally surrounded by people who do this for a living—and you're there to make their lives easier. In turn, they can be mentors and valuable resources. Whether you hit them up for advice on how to improve your writing, or ask what you can do to become better at Twitter, the people you intern for are much, much, more than just a potential reference or LinkedIn connection.
Know which talents and skills you hope to improve upon or gain.