Hi Igor. I will attempt to describe zanshin koshin in better detail, but I am no instructor so bear with me
We are taught that what you learn today you can teach tomorrow, so I'll take a crack at it. By lifting the leg so the thigh is parallel to the ground, potential energy is created. Zanshin koshin can be done to move both forwards and backwards. So if I wanted to move backwards, I would lift my front leg if I'm in a hanmi stance. The move backwards is initiated then by swiftly moving the leg in the air back and to the mat, so it becomes the back leg. But while you are moving the leg backwards, you sort of hop on the leg that you are standing on. So the leg that swings back gives the hop a lot of momentum, hence, a lot of distance can be covered very quickly. All this is done in one smooth, swift movement. Of course, to go forward this process is reversed, the rear leg being the leg that is lifted to create momentum. I hope this helps at least a little. It is actually quite simple, if I were to be able to show you in person it would make a lot more sense. I'm sure there are others who post on Aikiweb that could explain this better, but if I can help clear this up anymore just let me know.
Peace,
,
Joe