The specific use case was a repo centered around a python library that implemented a convenience API. To show how convenient, there are some demo notebooks to demonstrate it. I wanted to modify the demo notebook to remove a hard-coded path to the library, but just to make absolutely sure I was not introducing a problem, wanted to add an automated test.
More generally, one of the potentially powerful aspects of Jupyter notebooks is scientists collaborating on science workflows. So if I change something that makes a particular operation run faster (e.g., dask-izing it), it would be nice to automatically test the notebook (or that cell?) to verify the workflow still produces the same answer.
To take it one step further: if I obtained a result with a previous version of a dataset, it would be nice to re-run the workflow (or a particular cell) to see that I got the same (or similar result with a reprocessed version.