Get label for input field

Try to alert the contents of $label, you can use .text() for this

$('input').each(function(){
    var $element = $(this)

    if ($element.val() == '') {
        var $label = $("label[for='"+this.id+"']")
        alert($label.text())    
    }

}); 

Demo: Fiddle

Update

var $labels = $("label[for]");
var empties = $('input').filter(function(){
    return $.trim($(this).val()) == ''
}).map(function(){
    return $labels.filter('[for="'+this.id+'"]').text()
}).get().join(', ')

alert(empties)

Demo: Fiddle

Try

$('input').each(function(){
 if ($(this).val() == '') {

 $element = $(this)

 var $label = $("label[for='"+$element.attr('id')+"']")

 alert("You need to fill :" + $label.text())    

 }

 }); 

DEMO

Update :

is it possible to arrange all the $label in one alert() and not one alert() each?

Yes

var errorString ="";
var isNeedToFill=false;
$('input').each(function(){
 if ($(this).val() == '') {
isNeedToFill =true;
 $element = $(this)

 var $label = $("label[for='"+$element.attr('id')+"']");
  errorString += $label.text()+" ";
 }
 }); 
 if(isNeedToFill){
 alert("You need to fill :" +errorString);
 }

DEMO

Improving upon the answer you could wrap it in a function:

function getLabel(name) {
    var $label = $("label[for='" + name + "']")
    return ($label.text());
}

var label = getLabel(this.id);
console.log(label);

This makes it much easier to reuse the code.