The argument goes something like this: a CD has 16 bit audio, Blu-ray the same or more, which translates to a maximum dynamic range of 96 dB (or more for Blu-ray and other hi-fi formats). If your system is calibrated such that the maximum SPL you experience at your seat is 105 dB (I believe that's THX standard, and the reference level that is generally calibrated) you see that the quietest sounds on the disc could be as quiet as 9 dB, theoretically - but I understand that for other reasons 22 dB is the floor in most recordings. Why does that matter? Because if the ambient noise in your room due to the nearby highway or the refrigerator or the HVAC system exceeds that level (22 dB) you won't hear the full recording. If you turn up the volume to hear the quiet sections better, you can (very easily) run out of system headroom and power and end up with distorted blaring nastiness when the action gets going.
Realistically, a noise floor that low is an engineering marvel. Getting to that in a residential environment is impractical if not impossible, but that impracticality doesn't negate the benefits of trying. Check out the lengths forum member Digione went to in his build for some of the options that could be considered http://www.avsforum.com/t/1465163/my-a-v-room
On the other hand, lots of builds proceed with a single layer of drywall and fiberglass batts of insulation in the wall cavities - those theater owners are often very happy with the performance of their systems.
So, what does it cost? Well, that's tough to say as it will depend on the technical approach you take and the lengths to which you go. I think in my case, for my 2300 cubic foot theater, my sound isolation efforts add approximately $1500 to $2000 to the overall budget. In the context, I am happy with the investment. An extra layer of drywall, some Green Glue (which is not cheap), maybe some clips and furring channels can go a long way towards getting you a nice quiet room to build your sonic landscapes, but making that monetary investment means you have to make the commensurate investment in planning and execution time to be sure that you don't waste your money. A few errant screws or an open-backed light switch can undo a lot of your isolation. Even if you contract out the labor, you owe it to the investment (IMO) to educate yourself so that (at an absolute minimum) you can communicate clearly with your contractors about the appropriate use of the techniques and technologies you want to employ. Most professional builders and remodeling crews have not seen the sound isolation techniques used before, and they may even think that they are wrong or bad - you will have to educate them and follow behind them to be sure it's done properly.
This may all sound like a bunch of nonsense - and to the uninitiated it could easily seem so. I'm not trying to scare you off - all of this is DIYable with some research. You'd be surprised at the number of high-quality builds members put together here with very little prior experience; I hope mine is one of them one day.