Serializing an array in jQuery

You're not passing an array in proper format to $.param. From the jQuery.param docs:

If the object passed is in an Array, it must be an array of objects in the format returned by .serializeArray().

The array should be an array of objects consisting of name/value pairs. You see undefined=undefined&undefined=undefined because "val1".name, "val1".value, "val2".name, and "val2".value, are all undefined. It should look something like this:

[{name: 'name1', value: 'val1'}, {name: 'name2', value: 'val2'}]

So you can construct the array like this (assuming your checkboxes have a name attribute):

$('#rem_images').click(function(){
    var images = [];
    $('.images_set_image input:checked').each(function(){
        var $this = $(this);
        images.push({name: $this.attr('name'), value: $this.val()});
    });
    alert($.param(images));
    return false;
});

Even slicker, though, is to use .map() (because functional programming is good stuff):

$('#rem_images').click(function(){
    var images = $('.images_set_image input:checked').map(function(){
        var $this = $(this);
        return {name: $this.attr('name'), value: $this.val()};
    }).get();
    alert($.param(images));
    return false;
});

I find a great function to do that from another question https://stackoverflow.com/a/31751351/4110122

This function return array with key value pairs

$.fn.serializeObject = function () {
    var o = {};
    var a = this.serializeArray();
    $.each(a, function () {
        if (o[this.name] !== undefined) {
            if (!o[this.name].push) {
                o[this.name] = [o[this.name]];
            }      
            o[this.name].push(this.value || '');
        } else {
            o[this.name] = this.value || '';
        }
    });
    return o;
};

To use this just call:

var Form_Data = $('form').serializeObject();
console.log(Form_Data);

See the docs for $.param:

If the object passed is in an Array, it must be an array of objects in the format returned by .serializeArray()

[{name:"first",value:"Rick"},
{name:"last",value:"Astley"},
{name:"job",value:"Rock Star"}]

That means you need to generate your array in the same way:

$('.images_set_image input:checked').each(function(i){
    images.push({ name: i, value: $(this).val() });
});