Albert Barnes on Matthew 16:16

And Simon Peter answered, etc. Peter, expressing the views of the apostles, with characteristic forwardness, answered the question proposed to them by Jesus: "Thou art the Christ, the Son of the living God."

The Christ. The Messiah, the Anointed of God. Mt 11:14.

The Son. That is, the Son by way of eminence, in a peculiar sense. Mt 1:17. This appellation was understood as implying Divinity, Jn 10:29-36.

Of the living God. The term living, was given to the true God, to distinguish him from idols, that are dead or lifeless--blocks and stones. He is also the Source of life--temporal, spiritual, and eternal. The term living is often given to him in the Old Testament, Josh 3:10, 1Sam 17:26,36, Jer 10:9,10 etc. In this noble confession, Peter expressed the full belief of himself and his brethren that he was the long-expected Messiah. Other men have very different opinions of him, but they were satisfied, and were not ashamed to confess it.

(n) "and said" Ps 2:7, Mt 14:33, Jn 1:49, Acts 9:20, Heb 1:2,5