Onclick to store in array

Array.prototype.push is a method. You have to call it, instead of assigning a value to it:

function CheckBoxShortList(x,y,z) {
    var slide = '';
    var arr = [];
    arr.push(x + ',' + y + ',' + z); // length is 1
    console.log(arr);
    console.log('Length:', arr.length);
}

<input type="checkbox" onclick="CheckBoxShortList('a','b','c');">

This results in an array containing one string: ["a, b, c"].

If you want to push the values one by one, do:

arr.push(x); // length is 1
arr.push(y); // length is 2
arr.push(z); // length is 3

This results in an array containing three values: ["a", "b", "c"].

For removing it, use Array.prototype.pop:

arr.push(x); // length is 1
arr.push(y); // length is 2
arr.push(z); // length is 3
arr.pop();   // length is 2
arr.pop();   // length is 1

You can actually just use Array's slice function on an arguments object, and it will convert it into a standard JavaScript array

function CheckBoxShortList() {

    var arr = []; // whatever your array

    var args = Array.prototype.slice.call(arguments); // array

    arr.push(args.join(','));    // string you push

    console.log(arr); // show o/p

    console.log(arr.length); // it shows 1 because you are pushing only one element to array
}

<input type="checkbox" onclick="CheckBoxShortList('a','b','c');">

Earlier you were storing your values in an object named arr in its field named push.
Considering your values to be stored as a string in an array we call upon push method on it.

var arr = [];
function CheckBoxShortList(x,y,z)
    {
        var slide = '';

        arr.push(x + ',' + y + ',' + z);    
        console.log(arr);
    }

Considering your values to be stored separately

var arr = [];
function CheckBoxShortList(x,y,z)
    {
        var slide = '';

        arr.push(x);
        arr.push(y);
        arr.push(z);
        console.log(arr);
    }

define you array outside the function and fire your event onchange() instead of onclick()

 
    
    
    var arr = [];
    function CheckBoxShortList(x,y,z) {
        if($('#test').is(":checked")){
          var slide = '';
          arr.push(x + ',' + y + ',' + z);    
          console.log(arr);
        }else{
          arr.pop(x + ',' + y + ',' + z);
          console.log(arr);
        }
    }

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input id="test" type="checkbox" onchange="CheckBoxShortList('@item.Cid','@item.Hid','@k');">

As PeterMader said, Array.prototype.push is a method, it has to be passed the argument like this:

arr.push(x + ',' + y + ',' + z); 

If you wish to know why your code did not generate an error before it is because arrays are (obviously) objects in JavaScript. So when you says array.attr = value, the array object gets assigned an attribute attr whose value is value. In your case the array was assigned an attribute called push that stored your values, however, the array itself as a list was still empty which is why the array length was zero since additional attributes do not change the length of the array.

If you wish to add the items separately, you can use .push() for each item alone. You can also add another array to the original array using arr.contact(otherArray).

Hope that helps a little.