Sound isolation clips work by isolating the ceiling and walls from the building’s structure, so that the sound energy (vibrations) can’t pass directly through.
The metal clip is screwed into the wood or metal framing with a rubber isolator acting as the decoupler between the clip and the structure.
Rubber is really good at isolating two hard surfaces from each other, preventing any sound energy traveling through the framing from the floor above from passing through.
The other benefit of sound isolation clips is they allow you to create a larger air cavity between the two layers of drywall.
How much noise a wall blocks is a function of many things, and one of them is the size of the air cavity between the barrier on each side.
RSIC-1 clips allow you to increase the space by 1-5/8”, with some versions of the clip allowing for even more.