What are interviewers looking for when they ask "How would you test this"?

In a Software Engineering interview, oftentimes I come across the question "How would you test this?" after writing out the solution to their coding prompt. They always state they are not interested in functional/unit type of testing, so what kinds of answers are interviewers looking for?

For example, suppose the coding prompt was to write a function that returns a unique string abbreviation following a certain format for all strings passed in. Then you wrote the solution and then are asked what tests you would perform on this function disregarding functional/unit cases. How would you answer?