I think he means, that when a client make a request, the API server will now what version of the API it is calling, then whatever data the api call created/updated, the version of the the API being used will also be stored into the data.
One thing is that Stripe's documentation only shows the latest version, not the version of the API you are on. So for instance the API docs will show that the way you create a refund is charge->refunds->create(), but if your first request was before multiple refunds were a thing that api call would error since the api is expecting charge->refund().