The part of Jesus’s ministry that Isaiah 52:14-15 describes is his suffering and death, his resurrection, and the spread of the gospel after his ascension. Although the Gospel writers don’t specifically give the gory details of the condition of Jesus’s body from the time of his arrest until he is crucified, there are multiple references to him being slapped (Matthew 26:67, John 18:22, John 18:3), beaten (Matthew 26:67, Mark 14:65, Luke 22:63), and flogged (Matthew 27:26, Mark 15:15, John 19:1). After such treatment, it is easy to imagine that Jesus’s “appearance was so disfigured beyond that of any human being and his form marred beyond human likeness” and that there would be “many who were appalled at him.”
The word “sprinkle” is used throughout the Bible to signify cleansing, purification, and atonement. For example, Leviticus 8:11 (NIV) says, “He sprinkled some of the oil on the altar seven times, anointing the altar and all its utensils and the basin with its stand, to consecrate them,” and 1 Peter 1:2 (NIV) talks about “God’s elect…who have been chosen…through the sanctifying work of the Spirit, to be obedient to Jesus Christ and sprinkled with his blood.” Therefore, when Isaiah wrote, "he will sprinkle many nations," he meant that Jesus’s blood would cleanse and purify many people.