A private aircraft broker is someone who is knowledgeable in the field of private aviation: he knows the different types of aircraft, he knows the operators, the FBOs; he knows the airfields, the certification requirements. Whereas, most of the time, passengers who book private aircraft don't know these things.
So instead of asking your executive assistant (who usually has no knowledge about aviation) to book a flight, you would ask a broker.
The broker will always be with you along the way and solve unexpected problems: the operator will inform the broker of any unforeseen event and the broker will be there to find the best solution.
The broker will not only book your flight, he will make sure you have nothing to worry about from the moment you leave your home or office to the moment you get to where you're going. The broker will be in contact with your EA all the way: before the trip, he will provide a flight memo detailing all the information she (and you) need: transfer, driver's contacts, FBO information, tail number, pilot's and first officer's names and contact, possible refueling stops along the way, etc...
We are using very accurate software to track flight times and, based on that flight time, we used a second program designed by myclimate to calculate CO2 emissions. The database put together by myclimate comprises almost all the aircraft there is on the market and our calculations take into account taxi time, take-off, cruise flight and landing; but also Jet A1 production and delivery to the airfields.