That line is the target point for the middle of the grout line for
the next course that is aligned with the first to keep you running
straight ahead instead of letting the pattern shift as you proceed.

Ok, glimmer of understanding; hopefully, the book that RicodJour
recommended will have a picture. I have horrible images of my course
hitting the far wall canted at some extreme angle. ;-)

I'll wait until I read to the books before asking any more questions.

Thank you!