What type of curtains do I need to buy?
I've seen this style rod with pleated curtains. There are dozens of tall metal hooks that slip into pockets in the top of the curtain, then the hook sticks out of the curtain and goes through one of those holes. 

There should be cords on one side or the other that will allow you to open and close the curtains, similar to the pull cords for the blinds.

Apparently, they make hooks for this type of curtain rod that have pins that can go through a "regular" curtain to adapt it to this type of rod. This happens to be the first thing I found in a search that looked correct, so there's no particular endorsement of the vendor or the product, but it's an idea of what you're looking for in a hook. This means that you can buy pretty much any curtain and use these hooks.

This appears to be the more "traditional" type hook that I was thinking of. You can use these if you find a curtain that is designed for these. 

Sorry, I don't know the exact "name" for this kind of curtain.

Thanks to mattman944, I now know these are called "pinch pleat" curtains, and they hang on a "traverse rod". It's called a "traverse rod", I'd imagine, because when you pull the cord the curtains traverse across the rod. ;)