Hi Brian

I suspect that at some point you've 'pinned' the Search box and the Organisation to your desktop by clicking on the push pin in the top right hand corner. 

You can either click on the pin icons again (so that they point to the left rather than down) or click Start > Preferences > My Pinned Windows and delete them from there.

If that's not the reason, please send us a screenshot so we can get a better idea of what's going on.