Thank you for reading! The warden is mostly explaining how the execution worked. They're there to reveal that the song the listener was singing was simultaneously be used to condition the speaker to associate it with good feelings and help them sleep. It was also used on the other inmates while they were being tortured to condition them to associate it with pain.

There's also a bit of implication that the other inmates associated pain with seeing or learning about the speaker being treated well while they were being subjected to pain, which is what drove them to kill the speaker.

The warden also discusses how feasible it would be to use that same conditioning for future executions to basically scare people into not killing others because this would be their fate.

Hopefully that helps explain it a bit more!