The Pharisees asked John the Baptist, "Are you the prophet?" He said, "No, I am not" (John 1:21). The Pharisees were expecting the prophet referred to in Deuteronomy 18:18, but John said he was not that prophet. So to which prophet does Deuteronomy refer?
Judaic and Christian interpretations of this will differ.
Peter explained that the prophet to whom Moses referred was Christ, for whom Moses was himself an Old Testament type:
And he shall send Jesus Christ, which before was preached unto you: Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began. For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you.
(See also Acts 7:2ff)
"The evangelistic, or instructive, or prophetic ministry of the Lord Jesus Christ," writes one Orthodox Christian commentator, "was expressed in the fact that He proclaimed to men, in all the fullness and clarity available to them, the will of the heavenly Father, for the salvation of the world."* I have manifested Thy name unto men (John 17:6); I have declared unto them Thy name (John 17:26).
The Judaic interpretation, as one might expect, is markedly different, and seems to infer that Moses is really saying that multiple prophets will appear. A prophet, according to this interpretation, simply refers to the first prophet that will appear after Moses. One explanation, from The Oxford Jewish Study Bible (2nd ed.) reads:
The continuity of prophecy is assured by means of divine election. Other offices achieve their continuity by means of professional training and appointment (as with the judges of 16.18– 20; 17.2– 13), or dynastically (the king of 17.14– 20), or by tribal membership (the Levitical priesthood of vv. 1– 8). That God alone appoints the prophet makes the prophet independent of all institutions and able to challenge them. Yet the laws in vv. 20– 22, which emphasize various cases in which the prophets are to be executed, also curb the power of prophets, especially their ability to undo the contents of Deut.’s laws. A prophet, while grammatically singular, is likely distributive in its meaning: “I will repeatedly raise up for you a prophet.” More than one prophet is clearly intended.
This sentiment is also expressed in Rashi's medieval commentary (11th c.):
[A prophet] from among you, from your brothers, like me: This means: Just as I am among you, from your brothers, so will He set up for you [another prophet] in my stead, and so on, from prophet to prophet.
* M. Pomazanski, Orthodox Dogmatic Theology (3rd ed.), pp. 217-218