We know that all the prophets before Samuel also testified of Christ, Behold, I say unto you that none of the prophets have written, nor prophesied, save they have spoken concerning this Christ (Jacob 7:11). Therefore, we may find this to be a curious phrase. Why did Christ reference only the prophets since Samuel?
It is important to note that Peter taught the same thing in Acts 3:24. Peter was referring to the time when Christ would come again. He spoke of the times of refreshing which will not occur until the times of restitution of all things. He also stated that all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days. (Acts 3:19-24, italics added). Note how the text of Acts differs from 3 Nephi; Peter states that these prophets had all spoken of these days, speaking of the last days.
Therefore, although all the prophets may have taught of Christ, not all of them prophesied concerning the events surrounding his Second Coming. Samuel was the first in a string of Jewish prophets whose message was of the Millenial Christ. In anticipation of her son's ministry, Samuel's mother prophesied of the Millenial Christ, saying, The adversaries of the Lord shall be broken to pieces; out of heaven shall he thunder upon them (1 Sam 2:10). (Interestingly, this language closely resembles the language of 3 Nephi 20.) Therefore, the ministry of Samuel marked a shift in prophetic subject matter. From the days of Samuel to the days of Gordon B. Hinckley, the prophets would speak not only of Jesus of Nazareth, but also of the Millenial Christ.