When watching various streams, YouTube videos or LCS, I notice almost ALL the junglers doing this.
They attack, then turn away for a very very brief moment, the auto attack, then repeat this process until the jungle monster dies.
However, they are not soft resetting the camp, as they are not walking out to the boundary for the camp reset. They are still within melee range, but just turn away briefly then resume attacking.
This would make sense if they had somewhere to go to immediately afterwards and wished to in some sense 'kite' the jungle monster so they can get to the desired location faster. However, in terms of net position, they are pretty much not moving at all.
It appears that they take the same amount of damage, they don't seem to be auto attacking any faster so it can't be because of some sort of animation cancelling, so at this stage I see no advantages to doing this. One could argue that it's to make skillshots harder to land if there was an enemy out of their field of vision, but the movements are so minute that it doesn't seem like it will make any difference.
Why do they do this instead of just standing there and auto attacking?
I am happy to be corrected regarding my observations above. Perhaps they do take less damage, perhaps it does make a difference in terms of making skillshots harder to land etc.
Best Answer
One of the main reasons why they keep moving (and i do this as well) is to stay active. If you stay active while doing jungle creeps, you are trying to keep your focus on the game and are ready for anything that might happen (which most of the time is a kill attempt).
I don't think they do it for skillshot avoidance: If you keep moving, that might also mean you move into the skillshot.
For mitigating damage, the actual kiting after the first attack has almost no effect on your hp. (Note: I play a lot more Dota 2 at the moment [Eep!], where both skillshot avoidance and damage mitigation from jungle creeps can be important and is used more)
Lastly, All of these small things just add up to min-maxing of your time and staying active. Go into jungle camp, keep moving while attacking minions, find your next destination and get to the best position to move there, all the while you are staying active with the game.
(I'm still kinda new to SE, so tell me if i messed something up)
EDIT: I can't find the thread where a pro player mentioned they keep using the move command to keep active with the game, i can check later again. There are however some other threads about it. On the other side of the spectrum, your question was asked on the Dota reddit as well and got the same answers as on the LoL forums etc.
I can't link more than two things at the moment appearantly, so i kept the most important ones