It allows you to actually float that wall. The sheetrock is attached to the resilient member, which does not have a direct connection to the structural portion of the stud. So sound waves that hit the sheetrock, and even penetrate it, are essentially now isolated from being transmitted through the stud that is connected to the rest of the house. There's a vibration break. This is especially helpful for low frequencies where other types of systems out there don't do a very good job.
Low frequencies have long waves with lots of energy.
There are several advantages with the Acoustic Wall Framing over, say for example, a resilient channel. A resilient channel is a zee clip and works similar in fashion, except for the fact that there's more labor involved and you can pretty much be sure that you're going to short it out somewhere. The sheetrockers will come and short circuit the system, meaning that they'll drive their sheetrock screws through the resilient channel to a stud, so now it's short circuited by being directly coupled. And if you do that, you're negating the whole purpose of that system. With the Acoustic Wall Frame, this is pre-assembled lumber, so there's no way you're going to be able to do that.