In 18:15-19 Moses spoke concerning Jehovah God's raising up of a Prophet (the coming Christ) like Moses for the children of Israel. Acts 3:22 applies these verses to Christ, indicating that Christ is the Prophet promised by God to His people, the children of Israel.
The Prophet was to be from among their brothers (v. 15a). This indicates that Christ as the coming Prophet would be human as well as divine, that He would be God incarnated to be a man, the God-man. As God, Christ could not be from among the Jews as a brother, but as the incarnated One, the One who has put on human nature and who was a Jew, Christ was from among His brothers.
Moses told the children of Israel that they were to listen to this Prophet (Deut. 18:15b).
The Prophet raised up by God would be according to all that the children of Israel asked of Jehovah their God at Horeb (vv. 16-17). They had told Moses that they could not bear to hear God's voice. They wanted a middleman, one who could hear God's word and pass it on to them. Because they wanted a prophet, Moses promised that God would fulfill their desire for a prophet.
"I will raise up a Prophet for them from the midst of their brothers like you; and I will put My words in His mouth, and He will speak to them all that I command Him" (v. 18). This indicates that God would raise up this Prophet through the incarnation of Christ to speak the word of God (John 1:14; 3:34; 7:16-17; Heb. 1:2a). When the Lord Jesus came, He surely spoke God's word. To speak God's word is to dispense God, to speak God forth into others. This is what the Lord Jesus did as the Prophet raised up by God.