You can’t have clapping with one hand. By definition clapping involves two. In a very odd and funny way, this koan is telling us that everything is relationship and interconnects with everything else. You cannot have one hand clapping. It must always interact with another hand for clapping to exist.
In the same way, there are no sides to yin and yang. They actually flow together and interact. One cannot exist without the other and they are part of a whole. Yin, the feminine “side,” would not have anything to contrast with if the Yang, or masculine element, didn’t exist. Just as we would not be able to know what darkness was unless we also knew what light was.
The way the yin-yang symbol is designed gives a hint about this too, because it is a circle. If you move a circle around, the yin will be on top, to the left, slightly to the right—however you move it. There are no sides to a circle!