As Tony suggests in his discussion entry, this is the bulging of the sides of the cheese under its own weight as it softens on ripening.

This is a sign the affineur looks for in Brie (a flat disc), but applies to other varieties, such as the taller, firmer Charolais.

As the text says, the cheeses are also tapped or "sounded", which reveals much about their texture. Just saying that the cheese is "sufficiently matured" is to miss the point of how this is judged.

See: http://www.lowell.edu/users/grundy/cheese.html