c related

When you need to pass a function to another function. For example, qsort is written so that it can sort any data type, but you need to pass it a function that knows how to compare two elements.

Or when you want to change the function that gets called in some circumstances, e.g. when a button is pressed. Or if you want to re-implement virtual functions by hand.

Etc.

With modern C++ facilities, it's quite unusual to need it. When you do, you'll probably end up asking "how do I do this" and getting an answer about function pointers. Except that you'll actually probably more likely get an answer about functionoids (also called functors), because they're strictly more powerful.

Of course, if you really are stuck with C, you might need them a fair bit more (but again, not for everyday stuff). But then, why would you be stuck with C these days? :(