Yes, you can change the order of the tabs and blocks on your Page Profile from the “Edit Layout” section of your Page Dashboard. From there, you can move the widget blocks vertically up and down to change their ordering. You can also rename some blocks according to your choice. Some blocks might be “blocked” and would thus not be movable. This feature enables you to highly customize your Page, and allows you to give more prominence to that content for your Page which you feel has more relevance.
This setting is also monitored by our site administrators. You will not be able to change the ordering of tabs / blocks, if they have disabled the corresponding settings.