The title son of David signifies the kingdom. Christ, the son of David, is the King, the Ruler. As the son of David, Christ brings us into the kingdom of the heavens (Matt. 5:3).
Christ's being the son of David is also for us to participate in the divine authority. According to the Gospel of Matthew, the Lord Jesus has given us the authority to bind and to loose. "I will give to you the keys of the kingdom of the heavens, and whatever you bind on the earth shall have been bound in the heavens, and whatever you loose on the earth shall have been loosed in the heavens" (16:19). The Gospel of Matthew is concerned with the kingdom of the heavens, which is a matter of authority. The church revealed in this book represents the kingdom to reign. Hence, the authority to bind and to loose is given not only to Peter, the apostle for the church in 16:19, but also to the church itself (18:17-18).
Matthew 28:18-19 is another portion of the Word which reveals that we participate in the divine authority. "Jesus came and spoke to them, saying, All authority has been given to Me in heaven and on earth. Go therefore and disciple all the nations, baptizing them into the name of the Father and of the Son and of the Holy Spirit." Because all authority has been given to the Lord Jesus, the son of David as the heavenly King, He has sent His disciples to go and disciple all the nations. They go with His authority.
Christ is also the son of Abraham. In the Old Testament there was a clear prophecy that Christ would be the son of Abraham.
Isaac, the son of Abraham, was a type of Christ in three main aspects. First, Isaac brought the blessing to all nations, both Jews and Gentiles (Gen. 22:18; Gal. 3:16, 14). Second, Isaac was offered to God unto death and was resurrected (Gen. 22:1-12; Heb. 11:17, 19). Third, Isaac received the bride (Gen. 24:67). This is a type of Christ as the promised One who brought the blessing to all nations, who was offered to God unto death, who was resurrected, and who will receive His bride (John 3:29; Rev. 19:7).
As the son of Abraham, Christ brings us the divine blessing. Concerning this, Galatians 3:14 says, "In order that the blessing of Abraham might come to the Gentiles in Christ Jesus, that we might receive the promise of the Spirit through faith." The blessing here is the blessing promised by God to Abraham (Gen. 12:3). This promise has been fulfilled, and this blessing has come to the Gentiles, the nations, in Christ through His redemption by the cross.