
die Bestellung
order
A request to a company to deliver certain goods or provide a service, usually in exchange for payment.
Ich habe online eine Bestellung für neue Bücher aufgegeben.
I placed an order online for new books.
order / reservation
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order
A request to a company to deliver certain goods or provide a service, usually in exchange for payment.
Ich habe online eine Bestellung für neue Bücher aufgegeben.
I placed an order online for new books.

reservation
A reservation for a place, e.g. a table in a restaurant or an admission ticket.
Haben Sie eine Bestellung auf den Namen Schmidt?
Do you have a reservation under the name Schmidt?

cultivation
In agriculture, the working of the soil, especially the sowing of seeds.
Nach dem Regen war der Boden ideal für die Bestellung der Felder.
After the rain, the soil was ideal for the cultivation of the fields.

appointment
The formal appointment of a person to an office or official position. This meaning is rather formal or old-fashioned.
Die Bestellung des neuen Vorstandsmitglieds wurde in der Presse bekannt gegeben.
The appointment of the new board member was announced in the press.
'Die Bestellung' (the order/reservation) is the noun related to the verb 'bestellen' (to order/reserve). The ending '-ung' turns the action into a feminine noun that refers to the order or the process itself.
Die Bestätigung Ihrer Bestellung erhalten Sie per E-Mail.
You will receive confirmation of your order by email.
The many meanings can be distinguished well by context: If it is about goods, it is a purchase order. If it is about a restaurant, it is a reservation. If it is about fields, it is agriculture. If it is about an office, it is an appointment.
Meine Bestellung von Kleidung ist noch nicht angekommen.
My order of clothing has not arrived yet.
In connection with buying goods, the verbs 'aufgeben' (to place, as in placing an order), 'stornieren' (to cancel), or 'erhalten' (to receive) are often used.
Ich möchte meine Bestellung bitte stornieren.
I would like to cancel my order, please.
When you call a restaurant or hotel to reserve a table or a room, you can use 'Bestellung' (reservation). A typical question is: 'Haben Sie eine Bestellung auf den Namen Meier?' (Do you have a reservation under the name Meier?)
Guten Abend, ich habe eine Bestellung für zwei Personen für 19 Uhr.
Good evening, I have a reservation for two people for 7 p.m.
This meaning is very specific and is used almost only in agriculture. It describes work in the field, especially sowing.
Die Bestellung des Ackers muss vor dem ersten Frost abgeschlossen sein.
The cultivation of the field must be completed before the first frost.
Appointment to an office is referred to as 'Bestellung' (appointment). This usage is limited to formal, official, and legal contexts.
Die Bestellung zum Geschäftsführer erfolgt durch den Aufsichtsrat.
The appointment as managing director is carried out by the supervisory board.
assignment / order / mission
Auftrag and Bestellung can both refer to a business arrangement for the delivery of goods or the provision of a service. Bestellung emphasizes what a customer requests. Auftrag can also refer to this request, but it often focuses more on the work or service that the company is expected to take on and carry out.

Die Werkstatt erhielt die Bestellung über zwölf neue Fenster für das Haus.
The workshop received an order for twelve new windows for the house.
Die Werkstatt erhielt den Auftrag, alle Fenster des Hauses zu reparieren.
The workshop was commissioned to repair all the windows in the house.