That appears to be a gate valve. There is a threaded portion inside the valve that goes inside of a block of metal that moves up and down when you turn the handle. Since you can turn the handle, but the flow of water doesn't seem to increase, the gate has somehow become detached from the screw. Maybe the threads have stripped out, or maybe the screw shaft has broken.
Even if I'm wrong about the exact type of valve, that one is broken one way or another and will need to be replaced. Ball valves are a good choice for water heaters because they tend to be less likely to stick and are easy to turn off (only takes 1/4 turn). This shouldn't be a big deal using modern push-to-fit connectors on that nice copper pipe.
Feel free to post an additional question if you run into problems with the valve replacement.
Now that I think about it... Before anything else, try to push down with a good amount of force on the handle while turning the valve to open it. Perhaps you can get the threads to bite down and pull the gate up.