This one has a very simple premise. You have a single board, where you play on both sides of it simultaneously. I really should do a 3D image or something, but this illustration just shows both sides of the board (flipped, so the purple units are in the same column). On one side is the normal world, while on the flipped side is a demonic version of the world (flipped, of course). Basically, one side tries to kill the other side. Take turns moving units and attacking each other.

But wait, you say, if they are on two different sides of a plane, how do they fight each other? You notice that each side have two special units, a purple and green one (I'm questioning my color choice, but you get the point). They are special units. They cannot be killed, but they also cannot attack either. If they are targeted and hit, they will be pushed back a square in the opposite direction of the attack.

But if they aren't combat units, what do they do? They can flip specific squares from one side to the other. The green unit flips all the squares in the same row and column, while the purple unit flips all the diagonals. The green and purple flippers do not change sides at all, ever, but any other unit on a flipped square is moved to the other side regardless of which side he started on.

Here's an example. The purple dark wizard flips the diagonals (hopefully with a nifty little flipping animation) and delivers two of his units (one of which had already moved one square up and left) to the light side and brings two light units to the dark side. Now they can fight it out. It should also be noted that units benefit from being on the same colored squares. So a light knight on a light square will do significantly more damage than a light knight on a dark square.

Here, the green light knight (who has moved further than one could in a single turn, but this is an example) decides to do a flip, changing every tile in the same row and column. Notice that it inverts each tile rather than setting it to a specific side.