Chartering an airplane is best when you are flying with a large group and have time restrictions. One of the benefits of chartering a flight is that the airline will allow you to choose your departure time.
This helps in situations where you were unable to get your entire group on a flight at the preferred time.
Professional and collegiate sports teams often charter because they have specific time limitations and require a certain level of privacy.
One rather unknown benefit is that when you charter a plane, you have no checked baggage fees. If your group travels with a large amount of baggage, you may want to consider chartering a plane.