appointment
An agreed time to meet someone for something specific.
An appointment is an arrangement to meet someone at a specific time and place. When your parent schedules a dentist appointment, they've agreed to bring you to the office at, say, 3:30 PM on Tuesday. When your teacher makes an appointment to meet with your parents, everyone knows exactly when and where to show up.
Appointments help people coordinate their busy schedules. Without them, imagine trying to get a haircut: you'd have to keep showing up at the barbershop hoping they weren't busy. With an appointment, the barber reserves time specifically for you.
The word can also mean the act of choosing someone for a position or role. When a principal makes the appointment of a new teacher, she is officially selecting that person for the job. A president makes appointments of judges and cabinet members. In this sense, an appointment recognizes someone's qualifications and assigns them responsibilities.