Question: "What does it mean that Jesus is the Son of God?"
Jesus is not God’s Son in the sense of a human father and a son. God did not get married and have a son. God did not mate with Mary and, together with her, produce a son. Jesus is God’s Son in the sense that He is God made manifest in human form (John 1:1, 14). Jesus is God's Son in that He was conceived in Mary by the Holy Spirit. Luke 1:35 declares, “The angel answered, 'The Holy Spirit will come upon you, and the power of the Most High will overshadow you. So the holy one to be born will be called the Son of God.’”
During His trial before the Jewish leaders, the High Priest demanded of Jesus, “I charge you under oath by the living God: Tell us if you are the Christ, the Son of God” (Matthew 26:63). “’Yes, it is as you say,’ Jesus replied. ‘But I say to all of you: In the future you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven’” (Matthew 26:64). The Jewish leaders responded by accusing Jesus of blasphemy (Matthew 26:65-66). Later, before Pontius Pilate, “The Jews insisted, ‘We have a law, and according to that law He must die, because He claimed to be the Son of God’” (John 19:7). Why would His claiming to be the Son of God be considered blasphemy and be worthy of a death sentence? The Jewish leaders understood exactly what Jesus meant by the phrase “Son of God.” To be the Son of God is to be of the same nature as God. The Son of God is “of God.” The claim to be of the same nature as God—to in fact be God—was blasphemy to the Jewish leaders; therefore, they demanded Jesus’ death, in keeping with Leviticus 24:15. Hebrews 1:3 expresses this very clearly, “The Son is the radiance of God’s glory and the exact representation of His being.”
Another example can be found in John 17:12 where Judas is described as the “son of perdition.” John 6:71 tells us that Judas was the son of Simon. What does John 17:12 mean by describing Judas as the “son of perdition”? The word perdition means “destruction, ruin, waste.” Judas was not the literal son of “ruin, destruction, and waste,” but those things were the identity of Judas' life. Judas was a manifestation of perdition. In this same way, Jesus is the Son of God. The Son of God is God. Jesus is God made manifest (John 1:1, 14).