how update data through ajax and jquery

First of all, in your jquery event handler the action parameter’s value should be the string after wp_ajax_ and wp_ajax_nopriv_. So in your example the action should be update_records. So display_func is wrong.
Then in line 3 of your php code here the echo keyword should be removed.
So your php code should be like this:

function update_records(){
    global $wpdb;
    $id = $_POST['update_record'];

    $db_updated = $wpdb->update( $wpdb->prefix.'contact_form', 
        array(
            'names'  => $_POST['update_name'],
            'emails' => $_POST['update_email'],
            'gender' => $_POST['update_gender'],
            'age'    => $_POST['update_age']
        ), 
        array( 'ID' => $id ) 
    );
}  
add_action( "wp_ajax_update_records", "update_records" );
add_action( "wp_ajax_nopriv_update_records", "update_records" );