$.ajax context option

All the context does is it sets the value of this in the callbacks.

So if you’re in an event handler, and you want this in the callbacks to be the element that received the event, you’d do:

context:this,
success:function() {
    // "this" is whatever the value was where this ajax call was made
}

If you wanted it to be some other type, just set that, and this will refer to that:

context:{some:'value'},
success:function() {
    // "this" the object you passed
    alert( this.some ); // "value"
}

---

In the code you added to the question, you could use StateID, but you wouldn’t really need to since you already have access to that variable.

var StateID = $(this).parents('tr').attr('id');
$.ajax({
    url: 'Remote/State.cfc'
    ,data: {
        method:'Delete'
        ,'StateID':StateID
    }
    ,context: StateID
    ,success: function(result){

        alert(this);     // the value of StateID
        alert(StateID);  // same as above

        if (result.MSG == '') {
            $('#' + result.STATEID).remove();
        } else {
            $('#msg').text(result.MSG).addClass('err');;
        };
    }
});