It's useful to be able to pass functions. In C, the mechanism for doing so is the function pointer. Function pointers feel really complicated, relative to most other features in C, and relative to the mechanism for passing functions in other languages that allow it, but yeah, they do the job.

Consider, for example, how you'd pass a specialized comparator to a generalized quicksort function. In C, you pass a function pointer to a cmp() function. In Python you just pass a function, because functions are first-class values that you can use like anything else - you can pass it by name, or you can pass a lambda. In Javascript you can do like in Python, or you can declare a full-fledged function anonymously inline. In pre-8 Java, you have to pass a weird object that instantiates a class that has a static method with the right name; this is ugly as shit, but it does WORK. In Java 8 you've got lambdas, so that sucks less.

It's not like you can do anything you couldn't do before. It's just a little less stupid now.