The general idea is that it allows you to use constructions at a rather high level of abstraction and generalisation.
The arrow notation gives you a way of referring to a function (phrase) in a fairly general, abstract way, so that you can use it in other code, for example in a “To decide” phrase, which is itself a function.
The neat thing is that you don’t need to specify the actual concrete function (like squaring a number, or taking the square root, or the absolute), but can write the “framework” just with a placeholder, where you treat the function as a variable, so to speak.
That means that you can build a sort of “higher-order” function, for example a function that has another function as an input.
The classical example, which Dannii already mentioned, is “map”, which takes a function (let’s call it F) and a list as an input and applies it to each element of the list (and returns the resulting list). Map doesn’t care what the function F is and what the list is, as long as F’s input type and the type of the elements in the list match.
So, for a list of numbers, the function F could be squaring, taking the root, abs, and so on.
For an actual (though fairly specialized) “end-user” example, take a look at these posts from a thread sometime ago: Problems displaying values with units; math with values that have units generally - #3 by StJohnLimbo, Problems displaying values with units; math with values that have units generally - #5 by StJohnLimbo
In the context of Inform, it’s nice to know that the capability is there and to keep it in the back of your mind as another tool in the toolset, but don’t worry much about it. As the others said, it will usually not be necessary.
Side note:
If you are interested in programming in general, I’d recommend to look into the topic in more detail, because the “functional programming” style is quite important and interesting. From a practical perspective, it does have the reputation that it’s harder to understand in the beginning, but that it can contribute to clean code with very few bugs.
This is a nice tutorial for Haskell, one of the best-known functional programming languages, for example: http://learnyouahaskell.com/ (available as a book, but also free online)
Edited to add: Racket would also be a good choice to learn functional programming.