what is the point of var html = '';

With

var html = '';

you define that (html) is a string(text)-variable. ('') contains a specific, but empty text. After this definition you can add other strings (+ 'other string') to it later.

If you don't define this (html) as a string-variable, just only the variable:

var html;

it will give you an ugly "undefined"-Error in the output, since the script will try to add a string to a variable which isn't defined.

It's declaring an empty string variable to be used later. You can write it with either single quotes or double quotes.

var html = '';
var html = "";

and then later you might set it to something like

html = 'string';

or

html = "string";