Two cartilages form the tip of the nose, a left tip cartilage and a right cartilage.  In the before picture, you can see the depression, or dent, between her two tip cartilages.  They are quite prominent, and decreasing their strength was an integral part of obtaining this result.

If you don't mind looking at photos taken during surgery, the first chapter of the rhinoplasty surgery tutorial gives a good introduction to the anatomy of the tip cartilages,