Let's see if I can clarify it any..
Say you're holding a wash mitt and you're gonna wash the hood. The natural thing to do is to move your arm in a curving "sweep" type motion, covering maybe two feet or so.
Imagine a clock face. Mitt in your right hand. Typical arcing motion would be- if you're moving from left to right you might start around 7 o'clock, move up and clockwise towards 12 o'clock, and then come back down to around 4 o'clock. That "from 7 up to 12 and back down to 4" motion is the arc, like a semi-circle.
Better IMO to move straight, like from 9 o'clock right straight across to 3 o'clock.
IF something abrasive like a speck of dirt causes a scratch, a straight line scratch is only most obvious from one viewing angle while a curved/circular one is obvious from more viewing angles (thus always shows no matter where you're standing when you look at the car).
And long scratches are just more obvious than short ones so avoiding motions that cover a lot of ground is better IMO.
Look at some cars at the dealership and see how the scratches look. I bet you can see just how they happened..."wow, look at that long scratch, I can see just how his arm-motion must have been!". I think you'll see the "arc" that the mit/towel was moved in. The worst/most obvious example is "spiderweb" scratches like lots of circles.
Gee, this is harder to explain that I thought it'd be!