When you have added, removed or rearranged columns, you have adjusted the view that is used to display the structure. The view is marked as "adjusted" with the blue asterisk:
Saving View Adjustments
The adjustments you have made to the view are local, they are stored in your browser. To make the changes persistent and to push them to other people using the same view, you need to save a new version of the view. To do that, open Views drop-down and click Save link.
To save view changes you need to have Update access level for that view (see View Sharing and Permissions). If you do not have permissions to change the view, you can create a new view based on your modifications with Save As link.
If you need to remove your adjustments and get back to the original view as it stored on the server, click Revert link.
Sharing a View
A view has a set of permissions, just like a structure. When you initially create a view with Save As link, the view is private - it "belongs" to you and noone else can use it. You, however, can use this view with any structure.
To share a view with other people, you can either make view public, allowing everyone to locate and use this view, or define more fine-grained permissions for the view.
To make current view public, click Make Public link in the view drop-down. After that, everyone will be able to find and use the view, but only you will be able to modify it.
To define fine-grained permissions or modify sharing, click Share or Change Sharing link in the Views drop-down to open View Management dialog. See View Sharing and Permissions for details.