While wt1's example shows the die pinch crease entirely contained within the borders of the die, most do not. I like this example, which clearly shows the paper crease outside the die's border (view from inside the envelope):

The die interacts with the envelope blank from the top down. As the point of maximum pressure moves onto the head, the paper is pulled towards the center and is pushed down into the head. As the die rolls past the midpoint of the head that extra paper has no where to go, and a crease forms (or, is likely to form).
You can have a lot of fun collecting these. They are cheap efos (certain class of
ebay sellers notwithstanding), they work for cut squares, and you can make up lots of ways of classifying them.