The example @Jici listed works to ‘swap’ items, and this example shows re-ordering (similar to Trello):
The Trello re-ordering example uses two “Make Changes to a List of Things” actions each time a Thing is dropped, to make sure the elements above and below are always in the correct order, and that two don’t have the same Order field value at the same time.
Some forum posts suggest a different approach that involves dividing a Thing’s Order field by 2, but that can sometimes lead to two or more Things having the same Order field value (making it seem like it’s not working). There may be a better way with a different drag/drop plugin, but the above example is the only 100% Bubble way I know of that will make sure it works every time 