I'll quote my answer from this earlier question.
There is no such thing as a local function, actually. You are merely assigning variables that reference functions.
It's important to remember that functions are first-class values, and that all functions in Lua are anonymous (nameless). This code:
Is really sugar syntax (a nicer way of writing something else) for this:
And that this code:
Is really sugar syntax for this:
You might ask why it's not sugar syntax for this instead:
And the reason would be that you wouldn't be able to make recursive calls in the function if that were the case.
Again, functions are just like any other values in Lua. You can store them in variables, pass them to other functions, and so on, they're not special at all.