It is useful to save learning stories without sharing them with parents if you'd like to create a private record only visible for staff members, allow another staff member to review the learning story before it is sent or simply to save your work and resume it at later time.
Like described here you can decide to "Save" while creating a learning story, what this action does is to create a learning story that appears under the tagged children portfolio and is only visible for staff members.
Saved but not sent learning stories have a special button that allows you to resume your work:
By clicking the highlighted yellow button, the story creation screen will appear and you are able to resume the learning story.
After you are happy with your changes you can either 'save' or 'send' the story. If you 'save' the story it can be edited at a later date and guardians will not have visibility of the 'saved' story until it has been sent. Once a story has been sent it can not be edited.