First, if I understand you right, your question is "Why are functions first-class citizens in Kotlin -- And when to use them as such?", right?
Kotlin functions are first-class, which means that they can be stored in variables and data structures, passed as arguments to and returned from other higher-order functions. You can operate with functions in any way that is possible for other non-function values. (see here)
As stated in the docs, one use case are higher-order functions. As a first step, I will leave the wikipedia link here: https://en.wikipedia.org/wiki/Higher-order_function
Basically, a higher-order function is a function that takes functions as parameters, or returns a function.
This means that a higher-order function has at least one parameter of a function type or returns a value of a function type.
Following a short example of a higher-order function that receives a parameter of function type (Int) -> Boolean:
fun foo(pred: (Int) -> Boolean) : String = if(pred(x)) "SUCCESS" else "FAIL"
This higher-order function can now be called with any (Int) -> Boolean function.
The docs also state ... [can be used] in any way that is possible for other non-function values.
This means that you can, for example, assign different functions to a variable, depending on your current context.
For example:
// This example is verbose on purpose ;)
var checker: (Int) -> Boolean
if (POSITIVE_CHECK) {
checker = { x -> x > 0 } // Either store this function ...
} else {
checker = { x -> x < 0 } // ... or this one ...
}
if (checker(someNumber)) { // ... and use whatever function is now stored in variable "checker" here
print("Check was fine")
}
(Code untested)