The API support JSON as input/output.
For information about JSON goto Wikipidia - JSON.
Other formats may be avaliable for the individual ressources. Refer to the detailed documentation for the ressource for this information. Find link to the detailed documentation here
Content negotiation is a mechanism defined in the HTTP specification that makes it possible to serve different versions of a document. Wikipidia - Content negotiation
To get a JSON representation of the data you have the following two options:
$ curl -X GET -H "Accept: application/json" https://api.virk.dk/message/1.0/events
$ curl -X GET https://api.virk.dk/message/1.0/events.json