die Auslieferung
delivery
The handover of ordered goods to the customer; delivery.
Die Auslieferung der bestellten Bücher verzögert sich um zwei Tage.
The delivery of the ordered books is delayed by two days.

delivery / extradition
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delivery
The handover of ordered goods to the customer; delivery.
Die Auslieferung der bestellten Bücher verzögert sich um zwei Tage.
The delivery of the ordered books is delayed by two days.

The noun 'Auslieferung' (delivery / extradition) is derived from the separable verb 'ausliefern' (to deliver / to extradite). The ending '-ung' turns the verb into a feminine noun that describes the process or result of the action.
Der Händler konnte den Termin für die Auslieferung nicht einhalten.
The dealer could not meet the deadline for the delivery.
The context makes clear which meaning is intended. If it is about goods, packages, or orders, it means the delivery of goods. If it is about people, offenders, or the justice system, it means the handover to another country.
Wir warten seit einer Woche auf die Auslieferung unserer Möbel.
We have been waiting for the delivery of our furniture for a week.
In the context of goods delivery, 'Auslieferung' is often used with verbs such as 'erfolgen' (to take place), 'sich verzögern' (to be delayed), or in the phrase 'auf die Auslieferung warten' (to wait for the delivery).
Die Auslieferung erfolgt in der Regel innerhalb von drei Werktagen.
Delivery usually takes place within three business days.
In the legal sense, the preposition 'an' + accusative is often used to name the country to which a person is handed over. One fights 'gegen' die Auslieferung (against extradition) or agrees to it with 'zustimmen' (to agree/consent).
Die Auslieferung des Angeklagten an die USA wurde genehmigt.
The extradition of the defendant to the USA was approved.
delivery
'die Lieferung' and 'die Auslieferung' can both mean that ordered goods reach the customer. 'Lieferung' is the more general word: it can mean the whole process or the goods themselves. 'Auslieferung' puts more emphasis on the final step, that is, the handover or delivery to the customer. In many everyday situations, both are possible, but 'Lieferung' sounds more neutral and is more common. 'Auslieferung' is more precise when the point is that the goods are now actually being distributed or handed over to customers.

Die Auslieferung der neuen Fahrräder beginnt nächste Woche.
Delivery of the new bicycles begins next week.
Der Fahrer stellt die Lieferung vor die Haustür.
The driver leaves the delivery in front of the door.