One Inside Another

A composition feeds one function's output into another function. $g\left(f\left(x\right)\right)$ means: work out f(x), then use that result as the input of g. It reads "g of f of x", and books also write it as (g ∘ f)(x).

Take $f\left(x\right) = x+4$ and $g\left(x\right) = 3x$, and work out $g\left(f\left(2\right)\right)$. Inner first: f(2) is 6. Then g(6) is 18. Written out, f's rule turns the problem into $g\left(2+4\right)$, then g's rule gives $3\left(2+4\right)$, and the arithmetic finishes it.

Why the inside first? g needs a number to work on, and that number is whatever f produces. Code runs the same way: in g(f(2)), the computer calls f before g has an argument.