Question

When you scream into a pillow what happens to the sound waves?

Answer 1

I don't study sound waves in particular, but they are the compression and decompression of matter (usually air).

So your throat (somewhere in there, I'm no biologist, sadly...) does the compressing and decompressing the air, which pushes on the pillow. The pillow is more resistive to compression and decompression, so it does not compress and decompress as much. Thus, there is less sound emanating from the pillow. The compression and decompression might not get through the pillow, as the compression and decompression is resisted to the point of practically being nothing deeper into the pillow.

And I sides of you mouth are somewhat insulative (resisting compression and decompression) too. Much more than air!