Well... be prepared to handle it like it's a big job, not just an internship.
Mostly, places who hire interns start off by weeding out the people who seem like they are just looking for a name to put on their resume and don't care what they can bring to the table.
They'll try to weed out the people looking for a gateway to working at their company. That may be an internship to you... but them, most interns are cheap/free expendable labor.
Show them that you have dreams... tell them what you really want to do in the future and tell them how interning for them can fit in to those dreams.
Show them how you will be an asset to their company.
Be ambitious. Don't tell them you only want to do one certain thing. Tell them what you'd like to do there, but tell them what you'd like to take away from it. Despite the fact that they are looking for an asset, they don't want to hire an intern that isn't going to learn jack crap from working there.