$(this).val() not working to get text from span using jquery

Instead of .val() use .text(), like this:

$(".ui-datepicker-month").live("click", function () {
    var monthname =  $(this).text();
    alert(monthname);
});

Or in jQuery 1.7+ use on() as live is deprecated:

$(document).on('click', '.ui-datepicker-month', function () {
    var monthname =  $(this).text();
    alert(monthname);
});

.val() is for input type elements (including textareas and dropdowns), since you’re dealing with an element with text content, use .text() here.