Kukan is a Japanese term for the empty space, but there is so much more to this concept than just empty space alone. This is the space you move within, the space where you create techniques in response to the way the fight shapes, the puzzle you fit within as Nagato Sensei describes. This is also the space through which you project your intentions. We are always playing with the Kukan in class, even if one is not always aware of this. How the Kukan is shaped during a conflict is vital to understanding how to move and what to do. It is also what allows you to perform the techniques we train in the dojo.
Michael Glenn writes about this in his blog, for further reading I'll post the link to his blog because it is really a good post. Here is a quote from Soke he shares: "You've got to play in the space here. Be able to move freely, make your own kukan. Move with the opponent in the moment in a friendly fashion."
How does one make their own Kukan? You have your own space, it is not simply the Uke that creates the space. Think on the SanShin. Think of each of the waza in this kata. The Uke attacks, we move in the space, that is first and foremost, and there is some form of defense. But this shouldn't be though of as a block or deflection, it creates Kukan as well. So does your attack, but your attack will change based on the Kukan from your defense and from the Uke's response also (because an attacker won't stop after their first strike). So, you strike through the Kukan, strike the Kukan itself. Understanding this will make you far more efficient and effective.