Submitting data to public form/responses endpoints is a simple way to pass data from external systems into Gecko. Using these public endpoints allow you to control which fields can be updated, and bypass the need for authentication.
The easiest way to see the format that needs to be sent is to use the public form page with the network inspector open, look for the POST request to /responses and note the data that was sent to the various fields.
The 'uuid' is used to identify the form and is required, it can be found in the form share URL.
The utm_xxx, are optional and can be used to track referrers and PPC marketing data.
The fields object will vary per form, most field type use simple string values but you'll see the structure each field sends up by submitting the form.