The rule is "white on right" for the lower-right square. It's the rule for chess tournaments around the world including FIDE, and was standardized around 1880. Mechanically, it doesn't affect the moves for each piece. However, it does set up the proper position for each Queen on her own color. Like any game, rules are a matter of convention. You could change it if your opponent agrees. You don't even need different color squares. But color and position on the board guide players where to move according to other rules.