Here's the new feature in action:
This doesn't work for personal to-dos, of course, but if you create a named to-do list, for example for a specific project, then note the sharing control at the top right of the screen; (right) tapping the link brings up this sharing dialog. Tap the big blue button and sharing hooks will be set up on Microsoft's servers - this takes a few seconds.
Once done, the button changes to 'Copy link' and you can then share it onwards by any means you like (e.g. email) - anyone with the link can collaborate on the to-do list, adding, editing or deleting items; (right) after a few days, under 'More options', you can lock down the list to people who have already joined, just in case you're worried about the link being shared more widely and interlopers joining in.
You can grab Microsoft To-Do here in the Store, if you haven't already. This is shaping up to be a pretty powerful tool/service and I'll be diving into more depth with it in due course.