In items are either published or unpublished, and this property is displayed on the Edit Item properties panel.
In general, most views that you create in your story will be automatically set to filter out unpublished items.
This means that by marking items as unpublished, you can retain them within your story data, but prevent them from being displayed to other users on the views.
You can check the filter settings by accessing the filters (View Setup and then Filters).
In the screenshot below we can see that:
(a) the Published property has an 'active' status and
(b) the unpublished items value has been deselected.
This confirms that on this view, only items that have a property of Published will be displayed.
The Published property on forms
The Published property determines whether items submitted through the form will be assigned a value of published or unpublished.
So, your choice here is, 'Do I want the items that are created via the form to be immediately visible on my views?'. If the answer is Yes, then you can check the Published property.
If you leave the property un-ticked then any items created through the form will not be displayed on your views, allowing you to you first review them before deciding to publish them.
Reviewing / triaging un-published items
To review unpublished items in your story you have options:
(a) Temporarily change the filter on any view so that only the unpublished items (instead of the published items) are shown.
(b) In the date grid, unhide the Published column and then review the items, checking the box for any items you now want to publish
This will then create the column in the data grid called “Published” and you will be able to assess/filter items to their published status.