What it means is the "earned" their wings. They went through flight school, passed the tests, go the required number of aboves and graduated. They earned their wings.
Now occasionally, whether it be in the FRS or the fleet, it might be found that this individual is not performing to the level required or perhaps has done something stupid and negligent (flat hatting, etc....) What will happen is they will convene an FFPB (Field Flight Performance Board), review the aviators record, and decide upon one of several things: continue on, no more flying duties but keep your wings, or in the worst case, you lose your wings.
We had several guys go up for FFPB's in my fleet squadrons. What usually happenned is known as HAC and FAC (get your aircraft commander rating and then off to the ground side). Only once did we have to send a pilot to another MOS but even he got to keep his wings (sorry to see it happen - he was a good guy.)
Hope this helps out.