We are calling to 'confirm your appointment' with Dr. Jones. = We are calling to make sure that you will 'keep your appointment' with Dr. Jones.
The museum is open to visitors 'by appointment' only. [=you have to make an appointment to visit the museum]
The court ordered the 'appointment' of an attorney to represent the child.
(..) - vital to this country, which must be passed today! - Have I the floor? - I have lost all patience with him. I apologize for his appointment. I am sick and tired of this contemptible young man! I refuse to stay here and listen to him! I hope every member of this body feels as I do. (..)1939 Mr. Smith Goes to Washington
(..) from boys all over America. Senators, I have evidence that he owns the very land described in his bill. He bought it the day following his appointment to the Senate - - and is using his privileged office for his own personal profit! - Boy ranger had a racket. - This doesn't make sense. (..)1939 Mr. Smith Goes to Washington