Firstly ~ paper expands when wet. It has greater expansion across the grain.
Secondly ~ paper curls when damp.
Thirdly ~ paper folds better with the grain.
I shall expand on these paragraphs, with illustrations, when I get the time later in 2021.
More about this will be available under several headings. Craftworkers need to know all about it. Bookbinders do know all about it ~ it is one of the reasons why their training requires years of experience. Woodworkers also have to learn and respect and allow for grain ~ for many of the same reasons. Litho printers need to know about it.
~ Ways of finding the direction of paper's grain (2) wet it ~ 
~ Ways of finding the direction of paper's grain (3) ~ cheat .
~ Ways of finding the direction of paper's grain (4) ~ paste it .
~ Ways of not finding the direction of paper's grain (5) ~ guess it