You need to prevent the default action (the actual submit).
$(function() {
$('form#myForm').on('submit', function(e) {
$.post('mail.php', $(this).serialize(), function (data) {
// This is executed when the call to mail.php was succesful.
// 'data' contains the response from the request
}).error(function() {
// This is executed when the call to mail.php failed.
});
e.preventDefault();
});
});