The media type application/vnd.api+json refers to JSON API. You can read about it in great detail here.
In short, JSON API is an opinionated and well reasoned:
…specification for how a client should request that resources be
fetched or modified, and how a server should respond to those
requests.
The vendor prefix (vnd.) indicates that it is custom for this vendor. The +json indicates that it can be parsed as JSON, but the media type should define further semantics on top of JSON.