Right now runes are like having six different energy bars at the same time, one for each rune. The problem is that you must use a rune as soon as the "energy bar" is full or your "rune energy generation" will stop until you do, which causes a dps loss. The significant difference about the cataclysm rune system is that it pairs up each rune type into three energy bars of double length.
Lets say a blood dk wants to use heart strike. Ignoring death runes to keep it simple right now he has to blood runes to use it with. The problem is that both of them need to be kept on cooldown the entire time because rune generation doesn't happen when runes are not on cooldown. If he waits 3 seconds after each rune becomes available to use heart strike then he only gets to use it twice every 13 seconds instead of the potential twice every 10 seconds.
This is what the cataclysm system changes. Instead of two blood runes you start off with one blood rune energy bar at 2.0. using heart strike would drop that down to 1.0, would would then begin to regenerate. Using it again when you have 1.5 would drop it down to 0.5, which once again continues to regenerate. Now this is the important part, when that energy bar fills up to 1.0 you can use heart strike again, but you don't have to. It's like having one rune off cooldown, but there is no dps loss from not using it straight away because your rune energy generation is continuing at the same speed as it was before. Right now your rune generation is halved whenever you have one rune of that type available because only the other rune is regenerating and not both, the cataclysm system is different because rune generation continues at the full rate until both are available.
I'm not sure how useful that explanation is going to be to anyone, I have a decent picture of what it's going to be like in my head so I have no idea how well my post actually communicated that idea.
This post gives a reasonably good visual interpretation of the system if you find that more useful.