What exactly does an intern for a company do?

I want to be a Quora project manager in 1 - 2 years. I'm a college junior and am working as a project manager intern this summer at another technology company. What else can I do to make myself an attractive target?

• I'm studying chemistry and finance at an international university and taught myself programming. Also worked on a startup last summer and lead a nonprofit on campus. Quora is my dream company and I'd love to be part of the team. What else are they looking for that I can work on over the next year? NOTE: I know specific goals like this tend to be bad. I'm using Quora as an example, but this applies to similar companies as well.

• Answer:

  Build something on your own. Proof you know what you are doing, show that you are willing to work hands-on and try to get some connections to current Quora employees (but don't hassle them).