By using jQuery selectors for selecting the elements, you have a jQuery object and you should use val() method for getting/setting value of input elements. 
Also note that :text selector is deprecated and it would be better to trim the text for removing whitespace characters. you can use $.trim utility function. 
function checking() {
    var textBox =  $.trim( $('input[type=text]').val() )
    if (textBox == "") {
        $("#error").show('slow');
    }
}
If you want to use value property you should first convert the jQuery object to a raw DOM object. You can use [index] or get method.
 var textBox = $('input[type=text]')[0].value;
If you have multiple inputs you should loop through them.
function checking() {
    var empty = 0;
    $('input[type=text]').each(function(){
       if (this.value == "") {
           empty++;
           $("#error").show('slow');
       } 
    })
   alert(empty + ' empty input(s)')
}