The view of body hardening or conditioning, whatever you want to call it, is usually that of forging your body into "iron." The idea that you are forging your body into a tool by making it harder. I don't really believe this, but I have come to think of a different reason for practicing it, in a very limited and controled manner.
I believe it can be a replacement for full contact sparring.
In full contact sparring one hits and is hit at full force, but it is dangerous, unpedictable, usually requires at least some safety equipment, limits the techniques that can be used and realistically cannot be done all the time (every day or every practice session). The equipment itself can also change the way techniques are performed. Padded gloves/ headgear protect the hands from the hard skull, which create a artificial experience of punching somene in the head, and otherwise would be dangerous. The point of practice is to learn not to be injured or to injure. It also requires a partner.
Conditioning exercises can allow one to experience the pain associated with full contact sparring without all the unpredicatbility, allowing one to shrug off or at least work through the pain and give a person the confidence that they can get hit hard and keep on going. It also allows one to control the amount of intensity and increase it gradually. Depending on the exercise it also doesn't require a partner.
One could perform the slow sparring the Rory Miller suggests, slow movement with correct body mechanics to the intended targets, which allow for a safe, but realistic environment and full speed and power used on conditioning tools (makiwara, training dummies, or hitting each other in a controlled way) to replicate the pain and intensity of a real engagment.