The angel makes the relationship of John with the Elijah prophecy in Malachi very explicit. He does not want us to miss it. He will do what Malachi prophesied.
John is an answer to prayer for a faithful, childless old couple who, month after month, had lived with renewed disappointment. The angel prophesied a ton of joy! He was filled with the Holy Spirit from his mother's womb. God, fill my children with your Spirit.
The angel was also very clear with Mary that Jesus is the promised Messiah to sit on David's throne. He connected her child with the promise to Abraham in Genesis 12:1-4 and with the Davidic Covenant in 2 Samuel 7:13-16.