As hard as nails describes someone who is very tough or unfeeling, It could describe a patient who gets stitches without numbing, or it could describe a boss who refuses to allow a day off no matter how much you need it.
Before they were made in factories, nails were hand-forged from iron to be nearly indestructible. To be "as hard as nails" originally meant you had a "cast-iron" constitution — someone who could endure physical pain or hard labor without breaking. Today, we still use it to describe that same toughness, though it can also describe someone whose personality is as cold and unyielding as the metal itself.