What is the meaning of witnesses laid aside their robes at the feet of a young man Saul?

The account you're speaking of is found at Acts 7:58.

Saul, who later became the Apostle Paul, explains it at Acts 22:20

When God's servant, Stephen, was being killed for his support of Jesus, Saul was a young pharisee who hated Christians. When those who witnessed against Stephen prepared to stone Stephen to death (Deuteronomy 17:7), Saul was happy to watch their coats for them while they did the killing, feeling he was doing God's will.(John 16:2)(Acts 8:1).

Later, as the apostle Paul, he was sincerely sorry for these actions and was grateful for God's forgiveness.(1 Timothy 1:12-15)