Can someone explain this Kotlin expression.

Do I say, variable callbackFunction is of type Boolean, Or of type Unit
In that abstract function, is callback type of Boolean or Unit or something else?

The variable can be assigned a function that takes a boolean and returns Unit. The function takes as a parameter a function that takes a boolean and returns Unit

Does it mean variable is initialized by an empty anonyms function

{} is function that do nothing

Here you go:

protected var callbackFunction: ((Boolean) -> Unit) = {}

This variable is of type "function". In Kotlin, functions are first-class citizens, that means, you can use functions just like other variables --- pass functions as parameters to other functions, store functions in variables etc.

You can read that expression like this: "The variable callbackFunction is of type Function --- that accepts a Boolean and returns a Unit."

Later you can assign a function to the variable like this:

callbackFunction = { b: Boolean ->
    println("The value is a $b")
}

...or this:

fun showResults(b: Boolean){
    println("The value is $b")
}

callbackFunction = ::showResults   // assign by reference

Also, the variable is initialized by assigning an anonymous function like {}.

It's a lambda function that's the callback, it gives you back a boolean value whilst the function itself is Unit.

So somewhere in your code you'll have

startListening { it // this it will be the boolean returned from the callback

}

For more clarification read high order functions in Kotlin