Scroll on the page adds the class "ACTIVE" to the menu

Here's a suggestion:

Explanation:

• creates a addClass function to assign the class to li of the right menu
• Cache the li 's from the menu and the positions of each section , as well as each section
• listen for the event scroll and look for the menu element that corresponds ( i ) to the last section that have the position lower than the scroll (ie scroll has passed through it). Here ( if (scroll > this) ) can adjust with a numerical value so that if triggered sooner or later. For example: if (scroll > this - 100) will assign the class a little earlier.
• listen for the click also and add matching class

jQuery / JavaScript

function addClass(el) {
    menu.removeClass('active');
    $(el).addClass('active');
};

var menu = $('#meuMenu .nav li');
var sectionPositions = $('section').map(function(){
    return $(this).position().top;
});
var sections = $('section');
$(document).on('scroll', function () {
    var scroll = $(document).scrollTop();
    var currentElement;
    $(sectionPositions).each(function (i) {
        if (scroll > this - 50) currentElement = menu[i];
    });
    currentElement && addClass(currentElement);
});
menu.on('click', function () {
    addClass(this);
});

Now you only need to add in CSS (or use what you already have):

.active{
    border: 1px green solid; # ou outra propriedade que goste
}

You can also change the CSS directly in the element, using:

function addClass(el) {
    menu.find('a').css('color', 'inherit');
    $(el).find('a').css('color', 'blue');
};

Note: You have an error on line 129 of the index file:

Change:

$(nav navbar-nav menu a).removeClass('active');

for the code below (with quotation marks):

    $('nav navbar-nav menu a').removeClass('active');
//    ^                     ^

$(a[href^='#']).click(function(){
$(nav navbar-nav menu a).removeClass('active');
$(this).addClass('active');
return false;


 });

You need to detect the click on your menu and add a class, in the active case, as quoted, for example:

$('#meuMenu ul li').click(function(){
    $('#meuMenu ul li').removeClass('active');    
    $(this).addClass('active');

});

JSFiddle