I think, in a nutshell, if you are going to operate a private aircraft, then there are things that need managing. You will need some sort of operations manual, someone to monitor all the legalities such as RVSM, radio licenses and so on. You will need someone to manage the continuing airworthiness and finally, a provider for all of the flight planning necessities. You can, and many people do, get your chief pilot to do this for you. But a management company offer all of this under one roof, with economies of scale and also experience! If the company have an AOC, there is also the option of offering the aircraft to charter in order to recover some of the costs, although there are additional costs associated with this!
I hope this helps!