What are the advantages of the Airbus New Engine Option (NEO) program?
How does adding more options for engines for potential customers act as an advantage for the Aircraft Manufacturer?


There are a couple of ways of looking at this


Why new options?
Why multiple options


Change

The A320 has been around a while, engines have improved a lot and newer types of engine exist now that were not available before, even though the A320 type airframe is still competetive.

According to Airbus, new choice of engines allow for


Lower fuel costs
Lower maintenance costs



  Airbus is working on offering a new engine for the A320 known as the New Engine Option (NEO). The choice for new engines include the CFM International LEAP-X and the Pratt &amp; Whitney PW1400G/PW1500G. The new engines will burn 16% less fuel: the actual fuel gain on an A320 installation will be slightly less, since 1-2% is typically lost upon installation on an existing aircraft. Airbus CEO said to be "comfortable" with the projections of 20% lower maintenance cost for the Pratt &amp; Whitney's PW1000G family, compared with today's engines. 


From Airbus

Choice

Speculating a little: 

The people who buy and operate aircraft like having a choice of engine manufacturers. It helps keep the engine market competitive and it means they can, if they want, operate a range of aircraft all using engines from one maker - potentially allowing for savings in engine maintenance infrastructure.

Aircraft operators sometimes don't actually buy engines with their aircraft, they buy thrust from an engine maker and the engine maker (effectively) install their engines on the operators aircraft. The engines might remain the property of the maker.

It may also be that aircraft makers don't wish the future of their aircraft to be tied to a single supplier of engines. It makes negotiating harder and it makes their future prosperity dependent on the continued existence of one manufacturer.