When using a router to add a decorative touch to the curved edge of a piece of wood, tear out can occur in certain areas. In those areas, you can often avoid tear out by climb cutting with your router. This is one case where climb cutting instead of conventional cutting is advised.
This photo shows how to address curves on a router table.climb cutting.jpg
Here is what can happen when routing curves with conventional cutting. climb cutting router.jpg
See the explanations here and here.