How does diffraction enable somebody to hear your voice from anywhere in the room?

Diffraction means spreading out of waves that has the same wavelength as the size of the gap. Sound waves have high wavelength and so it diffracts\spreads out and enables anyone to hear your voice from anywhere outside the room.

For inside the room, the sound waves doesn't actually diffract. They collide with the air particles, causing a series of compressions and rarefactions which spreads out in the air particles and anyone can hear your voice.

Air is the medium for the sound waves to travel.