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A crease gives the card a hinge. As you close it, the inside of the fold compresses and the outside stretches. The shape of the crease helps the card bend along the centre line.
In print finishing, a rounded steel rule presses the board into a narrow channel. That single press leaves a shallow groove on one face and a small raised ridge on the other. In board made of several layers, the pressure can let those layers separate slightly at the crease, so they can bend more easily.
With the ridge inside, it compresses as the card closes. If you fold the other way, the ridge sits on the outside, where the surface has to stretch. If the surface splits, pale fibres can show through as a broken line. That line is especially easy to spot where dark print crosses the fold.
An 1876 US patent for folding paper boxes shows the same principle. Its drawings compare a fold with the ridge tucked inside against folds made in the opposite direction. The same concern matters when finishing printed greeting cards today. The fold needs to close cleanly without spoiling the printed surface.
