When you begin to dig in to Lambda Calculus, it kind of blows your mind, and this lecture, is by far the best presentation on the topic I have ever come across!
But it has me thinking... What's the point? Is the closure all there is to take away from this new world?
I've enjoyed the walkthrough of programming FizzBuzz without numbers:
In terms of practical applications it's as useful as Turing machines. Rust has slices, not tapes 
But it is a mathematical construct which helps reason about what programs can and can't do.
Lambda Calculus, what is it for?
I guess the first point is that whatever it is you are doing with a computer today it is equivalent to a Turing Machine, which just happens to be equivalent to Lambda Calculus.
See Church-Turing thesis: https://en.wikipedia.org/wiki/Church–Turing_thesis
On a more practical level check out how Mario Fusco reduces the last two decades of object oriented nonsense down to a few lines of lambda calculus based code: "g ∘ f patterns by Mario Fusco" : https://www.youtube.com/watch?v=Rmer37g9AZM