What does k stand for here? As someone that never encountered this
function before I find both names equally confusing. If I understand
what the function is supposed to be doing, I think largest() would be
much more descriptive.
`k` is the number of elements to return. `largest()` can connote that it's only returning the one largest value. It's fairly typical to include a dummy variable (`k` or `n`) in the name to indicate that the function lets you specify how many you want. See, for example, the stdlib `heapq` module's `nlargest()` function.
"top-k" comes from the ML community where this function is used to evaluate classification models (`k` instead of `n` being largely an accident of history, I imagine). In many classification problems, the number of classes is very large, and they are very related to each other. For example, ImageNet has a lot of different dog breeds broken out as separate classes. In order to get a more balanced view of the relative performance of the classification models, you often want to check whether the correct class is in the top 5 classes (or whatever `k` is appropriate) that the model predicted for the example, not just the one class that the model says is the most likely. "5 largest" doesn't really work in the sentences that one usually writes when talking about ML classifiers; they are talking about the 5 classes that are associated with the 5 largest values from the predictor, not the values themselves. So "top k" is what gets used in ML discussions, and that transfers over to the name of the function in ML libraries.
It is a top-down reflection of the higher level thing that people want to compute (in that context) rather than a bottom-up description of how the function is manipulating the input, if that makes sense. Either one is a valid way to name things. There is a lot to be said for numpy's domain-agnostic nature that we should prefer the bottom-up description style of naming. However, we are also in the midst of a diversifying ecosystem of array libraries, largely driven by the ML domain, and adopting some of that terminology when we try to enhance our interoperability with those libraries is also a factor to be considered.