Thanks, so application comes down to plugging in values, I got as far as "plugging in values" in the subject document (except that I didn't realise that's what application meant).
Then I kind of recoiled from reforming, say f(x) = x^2 + 1 so f(1) = 1^2 + 1 = 2 into something seemingly more complicated for reasons that are difficult to discern for me as a reader and no doubt difficult to describe as an expert writer. I have the same difficulty with your last paragraph.
The idea is that it's a set of basic rules that can be used to model any computation (lambda calculus is Turing-complete). So think of it as a programming language with a very minimal set of primitive/builtin operations, which is really what it is.
The reason things can seem more complicated than they need to be is that this set of primitive operations is so minimal; and the reason it's so minimal is that Alonzo Church came up with it in the 1930s when they were trying to get to the very bare bones of the concept of computation.
Lambda calculus is the grandfather of all functional programming languages. Lisp was a more or less direct implementation of it
Then I kind of recoiled from reforming, say f(x) = x^2 + 1 so f(1) = 1^2 + 1 = 2 into something seemingly more complicated for reasons that are difficult to discern for me as a reader and no doubt difficult to describe as an expert writer. I have the same difficulty with your last paragraph.