The response to your request can be found at a different URL, and you should fetch it with GET.
303 See Other is the "POST/Redirect/GET" status code. It is the canonical way to redirect after a form submission: the client POSTs to /submit, the server processes the data and responds with 303 pointing at /thanks; the browser does a GET on /thanks. This avoids the duplicate-submission problem (refresh the page after a POST and most browsers warn "do you want to resubmit?"). With 303, refresh just reloads /thanks, which is idempotent.
When servers should return it: Return 303 after a state-changing POST or PUT, when you want the client to GET a different URL to see the result. Always pair with a meaningful Location header.
curl -i -X POST -d "name=Ada" https://example.com/users
HTTP/2 303
location: /users/42
For a one-page reference of all HTTP status codes, see the HTTP cheat sheet. For testing API responses, try the API Tester tool. For inspecting responses on the command line, the curl cheat sheet covers the most common flags.