Nice explaination,
bookworm 
That was the rational behind the design of the HSI - by spinning the CDI (
Course Deviation Indicator) needle around a compass rose, and slaving the compass rose to the aircraft heading, the HSI became a
"command" instrument - for VORs it
always operates in the command sense. All you have to do is look at it after setting up your radial to understand your current position with respect to that radial.
It saved all the mental combobulations involved with a fixed CDI display.
As both VOR and ILS systems show your displacement from a line based on the phase difference between two radio signals, the same CDI has always been used for both systems. With an ILS signal, the "radial" is fixed, so the OBS isn't used by the system at all - it just detects the phase difference, and displays that on the needle. For the old fixed CDI display, it didn't matter what you put on the OBS when flying an ILS - as this bit isn't used at all by the ILS.
Then the HSI came in, and the CDI turns around with the aircraft's heading. Now when using the ILS you need to set up the needle so that it points "up and down" with respect to the panel for it to operate in the command sense, and the only way to do that (as it rotates on a slaved compass card) is to set the OBS to the track you are going to be flying when you are established on the ILS (i.e. the inbound track).
For ILS the two lobes, the "left" and "right" lobes, are set up to display correctly for front course (the most common) approaches. If you are flying an approach to the reciprocal runway you are pointing the aircraft 180º in the opposite direction for the approach - but the ground staff haven't run out, dug up the Localiser antennae and spun them around 180º for you! The "Left" and "Right" lobes are therefore 180º out of sync - so you need to turn the CDI "upside down" to correct that. (Or flip the backcourse switch on the old fixed CDI indicator to reverse the sense.)
