My guess is it's "roughly a quarter of the total map space". That's how I interpreted it.
Oh damn, that's a good point. My other guess would be "a zone created by the lines your drew". In fact, a deeper search of the book I did just now found me this:
"Quadrant size
If you have relatively equally sized quadrants
you can consider them to have an area of about 1
square kilometer."
That definitely seems to imply that a quadrant is meant to be one of the zones formed during step 1.3.