The surgeon tunneled under the skin over the bridge of the nose and made alterations almost blindly. This is called a closed rhinoplasty because all of the incisions are enclosed inside the nose. It’s a bit like trying to carve a delicate glass figurine (the nasal cartilage) while working under a blanket (the skin).
Then some bright guy came up with idea of carrying a very small incision across the columella or skin bridge that separates the two nostrils. This allows the entire skin over the nasal cartilage and bone to be lifted up to see what’s underneath. This technique is called an open rhinoplasty or external rhinoplasty.