Correctness testing, or testing for functional correctness is the comparison of a current API result to a previous "correct" result, and comparing for differences.
Good monitoring tools let you save the expected result of your API request and compare the results at certain intervals. You then optionally get a notification if your API is returning incorrect data, or data you did not expect.
Why should you care?
If data changes shape in a way you didn't expect, you'd want to know about it. functional correctness testing also lets you monitor the "contract" between front-end and back-end, and if your back-end team changes the way it sends data, your front-end team will definitely want to know about it!