When the admin changes(Add/Remove) roles of the user, how to get assigned and removed roles of that user?
Implement hook_user_presave:



/**
 * Implements hook_user_presave()
 */
function yourModuleName_user_presave(&$edit, $account, $category){
  foreach ($account->roles as $role_id => $val) {
    $user_roles_existing[] = $role_id;
  }    
  foreach ($edit['roles'] as $role_id => $val) {
    // $edit['roles'] contains all roles ids as key and selected role id as val. If not selected then value is 0
    // ex. $edit['roles'] = array(5=>5, 6=>0) here role id 5 selected
    if ((int) $val > 0) {
      $user_roles_form[] = $role_id;
    }
  }    
  $user_roles_new = array_diff($user_roles_form, $user_roles_existing);
  $user_roles_removed = array_diff($user_roles_existing, $user_roles_form);     
  //roles added
  if (count($user_roles_new) >= 1) {
    /**
     * Required code...
     */
    drupal_set_message('Testing new roles count' . count($user_roles_new));
  }
  //roles removed
  if (count($user_roles_removed) >= 1) {
    /**
     * Required code...
     */
    drupal_set_message('Testing Removed roles count' . count($user_roles_removed));
  }
}