How does a JavaScript function store local variables after being called?

Question

I came upon this simplified example of a memoization function in JavaScript. It's then used to memoize a function that adds 2 to whatever number is passed in. When I saw this, it didn't seem obvious that the memoize function would continue to store the cache variable after being ran since it's not a property of memoize, just (seemingly) an ordinary local variable. Shouldn't it be overridden whenever memoize is called via plusTwo? Where can I find out more about this behavior in JavaScript?

var memoize = function(function_) {
    var cache = {};

    return function() { // What does this function do?

        //makes a string out of the arguments of the function that was passed in
        var arg_str = JSON.stringify(arguments);

        /* 
        sets the cache value for the arguments to the value that was already calculated 
        (if available) or calculates the value for the passed in function on its
        */
        cache[arg_str] = cache[arg_str] || function_.apply(function_, arguments);

        console.log(cache);
        // returns the calculated (or cached) value
        return cache[arg_str];
    };
};

var plusTwo = memoize(function (x) {
    return x + 2;
});

module.exports = memoize, plusTwo;