Forewarning: This vid looks fake and somewhat silly. When you get into the realm of aiki, things look fake and silly on video. This vid shows a good reason why videos on aiki aren't really useful. It's all internal.
So, the explanation as I put on Youtube.
In this video, I'm using intent to internally turn my spine. From my internal intent and connection to uke through the wrist grab, uke feels the effects and is displaced either left or right, depending on if I'm turning clockwise or counterclockwise. I try not to move physically as this is an intent driven exercise.
Once you start building structure, it starts to remove slack in the body. Slack you never knew you had. It integrates the body into a whole. For example, shoulder joints are notorious for being disconnected. Structure training corrects this (or should if you do it right and quit trying to use your chest muscles to drive movement -- sorry, personal experience). Current theory is that this training involves fascia. I'm no physio PhD, so I'll leave all the theories to other people. The Chinese call some of this training tendon changing or marrow changing or both. Dunno. It's just training to make the body work differently and to be able to receive and generate more force/energy.
Now, once you start building this structure, you start using "intent". I like the Ki Society unbendable arm example here. You're told to imagine your arm is a firehose and water is flowing out the hose. You are using intent, or imagination, to get your body to do something specific. If you tense your biceps while doing this exercise, things fail.
NOTE: You can view this Ki Society example of intent as being the very tip of one snowflake sitting on top of the very tip of a large iceberg. That's how deep and huge aiki is, IMO.
In this video, I'm using another intent exercise. This time, I have a semi decent push coming in from uke. Not full force but not light. Enough to get me to have correct structure but not to cause me to fail and be pushed over. (Video doesn't show levels of force or how that force is generated.) I'm then using intent to turn my spine either clockwise or counterclockwise while physically remaining in place. I'm not thinking about uke or trying to get uke to move. It's all internally driven around me.
Intent isn't aiki. It's like structure, another component of aiki.