The abstract of the VAPID specification explains everything:
An application server can voluntarily identify itself to a push
service using the described technique. This identification
information can be used by the push service to attribute requests
that are made by the same application server to a single entity.
This can used to reduce the secrecy for push subscription URLs by
being able to restrict subscriptions to a specific application
server. An application server is further able to include additional
information that the operator of a push service can use to contact
the operator of the application server.
So there are two reasons for VAPID.
The first is to restrict the validity of a subscription to a specific application server (so, by using VAPID, only your server will be able to send notifications to a subscriber).
The second is to add more information to the push notification, so that the push service operator knows who is sending the notifications. If something is going wrong with your notifications, the operator knows who you are and can contact you. Moreover, they can offer you some kind of interface to monitor your push notifications.