If you play with premoves on, then you'll possibly use this feature. If you premove while waiting for the opponent to move, then you can right-click the square to un-premove it (red square shows premove square). It is seldom used, but maybe you premoved the wrong move (or change your mind) - undo it quickly before your opponent moves!
If you have premoves off, then I think the squares mean nothing if red. Premoves are essential in fast time controls if used correctly, but not as necessary for longer games.
Maybe someone streaming online wants to show what they are thinking and so they use arrows and highlighted squares. Maybe the red squares could be used for other reasons too, but I can't think of any others at the moment.
I noticed that you can change the squares to be temporarily red or yellow by right-clicking.
Do you actively use this feature during your games, and in what way/during what circumstances?