Defines the parent to the service, which is almost always paired with abstract services. This is implemented in the service as either normal inheritance or as a trait. For instance:

entity.manager:
 class: Drupal\Core\Entity\EntityManager
 parent: container.trait 

defines the Drupal\Core\Entity\EntityManager class, which uses the Symfony\Component\DependencyInjection\ContainerAwareTrait.