Yes O(f(n)) shows how the function f(n) is upper-bounded, but the point of the comment you're replying to is that the function f could be the worst-case, average-case, or best-case running time of an algorithm, or even a (say) number-theoretic function that has nothing to do with running times. (More here: https://stackoverflow.com/a/1960493 including the example in the comments of an algorithm whose best-case cost is O(n^2) and worst-case cost is Ω(n^3) — it is perfectly meaningful to give an upper bound on the best case, and a lower bound on the worst case.)