The Hebrew word מוּסָר mûsâr (moo-sawr) is used in Isa 53:5 and means chastisement,
which in Hebrew means instruction, training, correction given by parents upon their children to perfect-to complete them. Chastisement includes learning by suffering. One can chasten his son by causing him to suffer to one degree or another with the purpose to teach him something that he might otherwise not learn. This is called discipline as well.
Now that Isa 53:5 has been fulfilled, we know God told man ahead of time He would perfect His Son to be the Author of Salvation through the sufferings that brought us peace with Him. Our Lord's real experiences of humbling Himself to come into our form and living in our human weakness, suffering and giving up His life unto death on account of our sins is what purifies us of our sins and reconciled-restored our relationship to God.
Here we are informed that God made our Lord, the Author of our salvation "perfect" through suffering.
"For it was fitting that he, for whom and by whom all things exist, in bringing many sons to glory, should make the Author of their salvation perfect through suffering." (Heb 2:10)
Again, we are informed that our Lord "learned obedience through what He suffered", and was "made perfect" by it, becoming the source of salvation.
"In the days of his flesh, Jesus offered up prayers and supplications, with loud cries and tears, to him who was able to save him from death, and he was heard because of his reverence. Although he was a son, he learned obedience through what he suffered. And being made perfect, he became the source of eternal salvation to all who obey him, being designated by God a high priest after the order of Melchizedek." (Heb 5:7-10)
Here we are informed the oath of God "appoints a Son forever who has been perfected".
"For such a high priest was fitting for us: holy, guiltless, undefiled, separated from sinners, and made higher than the heavens; who doesn’t need, like those high priests, to offer up sacrifices daily, first for his own sins, and then for the sins of the people. For he did this once for all, when he offered up himself. For the law appoints men as high priests who have weakness, but the word of the oath which came after the law appoints a Son forever who has been perfected." (Heb 7:26-28)
The Hebrew understanding of chastisement does not mean penal punishment like us westerners have been led to think. It means instruction, training, or correction to perfect a person, to make them complete.
The suffering and death that Jesus our Lord experienced taught Him in all ways what it was to be in the weakness of humanity, so that He could fully sympathize with us; this being what He learned that qualifies Him to be "the source of eternal salvation for all who obey Him". This chastisement-being perfected through suffering-was upon Him for our peace, for our sakes ulitmately.
God Bless