Functions and Lambda Notation
A function accepts input and produces an output. Suppose we have a "chocolate-covering" function that produces the following outputs for the corresponding inputs:
peanuts -> chocolate-covered peanuts
rasins -> chocolate-covered rasins
ants -> chocolate-covered ants

We can use Lambda-calculus to describe such a function:
Lx.chocolate-covered x

This is called a lambda-expression. (Here the "L" is supposed to be a lowercase Greek "lambda" character).
If we want to apply the function to an argument, we use the following syntax:

(Lx.chocolate-covered x)peanuts -> chocolate-covered peanuts

Functions can also be the result of applying a lambda-expression, as with this "covering function maker":

Ly.Lx.y-covered x

We can use this to create a caramel-covering function:
(Ly.Lx.y-covered x)caramel -> Lx.caramel-covered x
(Lx.caramel-covered x)peanuts -> caramel-covered peanuts

Functions can also be the inputs to other functions, as with this "apply-to-ants" function:

Lf.(f)ants

We can feed the chocolate-covering function to the "apply-to-ants" function:
(Lf.(f)ants)Lx.chocolate-covered x
-> (Lx.chocolate-covered x)ants
-> chocolate-covered ants

What you're doing here is that you're actually associating the lambda with the operation of "x+ 1". You then associate the function f with this lambda.