"cached iteration over another iterator" means this iterator is always one step behind the inner iterator. In other words, the "first" iteration will yield null:

<?php

$cit = new CachingIterator( new ArrayIterator( [ 'a', 'b', 'c']  ) );

echo $cit->current() ); // null
echo $cit->getInnerIterator()->current() ); // "a"

while($cit->hasNext()){
    
    // we start with a "next" since the "first" item is null
     $cit->next();
     echo $cit->current(), '<br>';
   
}
?>

iterating this way gives us an access, ahead, to the future item (aka current item of the inner iterator)