What is the point of having lots of different flaps settings?
1a. On take off, with a light airplane you may select less flaps to reduce the additional drag and save some fuel. Max takeoff flaps are reserved only for short runways and high loads. Fuel savings are very important nowadays. 

1b. On approach, less flaps produce less noise and may also allow a higher approach speed (VFE is the maximum flaps extended speed and may be different for different flap settings). Maximum flaps are set only later in the approach when the plane has stabilized at the final approach speed. 

1c. The flap setting has an effect on the airplane's pitch angle. A certain flap setting may help to minimize the tailstrike risk. The longer B787-9 has nine settings, while the shorter 787-8 has six.     


I learned the Boeing numbers are not true angles either. For example, settings 1 and 5 may only affect the leading edge slats. At higher settings they approximate the actual angles (which are anyway somewhat misleading in the case of today's multi-part Fowler flaps, which move both down and backwards). 


https://www.flightglobal.com/news/articles/farnborough-aero-secrets-of-boeings-new-dreamliner-401784/

http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_08/pdfs/AERO_Q408_article05.pdf