Higher order functions. Consider a simple reduction operation, summing the elements of an array. In an imperative language, programmers typically write themselves a loop and perform reductions one element at a time.
But that code isn't easy to make multi-threaded. When you write a loop you're assuming an order of operations and you have to spell out how to get from one element to the next. You'd really like to just say "sum the array" and have the compiler, or runtime, or whatever, make the decision about how to work through the array, dividing up the task as necessary between multiple cores, and combining those results together. So instead of writing a loop, with some addition code embedded inside it, an alternative is to pass something representing "addition" into a function that can do the divvying. As soon as you do that, you're writing functionally. You're passing a function (addition) into another function (the reducer). If you write this way then it not only makes more readable code, but when you change architecture, or want to write for heterogeneous architecture, you don't have to change the summer, just the reducer. In practice you might have many different algorithms that all share one reducer so this is a big payoff.
This is just a simple example. You may want to build on this. Functions to apply other functions on 2D arrays, functions to apply functions to tree structures, functions to combine functions to apply functions (eg. if you have a hierarchical structure with trees above and arrays below) and so on.