Back beam procedures now only exist in Canada (I think) and are particularly prevalent on the East Seabord airfields where the predominant wind is Westerly, but if there is an Easterly off the ocean the weather is far worse and you need the lower minima.
The reason you set the reverse course is that the ILS does not transmit a radial like a VOR, but a fly left or right signal. If you are flying down the back beam, you would receive the fly right signal when right of the CL, i.e the wrong way. By turning the HSI course to the inbound QDM, you are effectively reversing the indication to make life easier.
Some instruments (like the 747-400 standy horizon which has ILS indications built in) have a sense reverse switch to provide the correct indications.