to issue (an official document)
to hand over (a certificate, permit, etc.)
La mairie m'a délivré mon nouveau passeport ce matin.
The town hall issued my new passport this morning.
to free, to rescue (from captivity, danger)
to relieve (figuratively — of a burden or worry)
Les pompiers ont délivré la famille coincée dans l'ascenseur.
The firefighters rescued the family trapped in the elevator.