JOEL -
Nephi 21:1 "And there shall come forth a rod out of the stem of Jesse, and a branch shall grow out of his roots;"

First of all the D&C makes it quite clear that the "stem" of Jesse is Jesus Christ (DC 113:21-22). Actually, the "branch" mentioned by Isaiah is probably just another word for "stem" and therefore also refers to Christ. It then goes on to describe the attributes of the person or persons who represent the "rod" and the "root", without giving any names (DC 113:3-6). Many LDS scholars have interpreted this description as one that applies to Joseph Smith. After all, it is a pretty good representation of the mission of Joseph Smith here on this earth. It also explains why the angel Moroni quoted this Isaiah scripture to Joseph Smith when he appeared to him. However, to my knowledge there has never been any recent "official" interpretation by the leaders of the Church as to who the scripture is talking about. The 'root of Jesse' could also be that particular prophet who will hold the keys when Christ returns to preside personally over his kingdom. The term could even represent the office of the president of the Church. In any case, the 'root of Jesse' designates a great leader in the Church of Jesus Christ in this dispensation. On the other hand, many other Christian religions use the translation of Isaiah, which reads, "a shoot will come up from the stump of Jesse"(Isa. 11:1). They interpret this as the House of David being the "stump"(stem) and Jesus as the "shoot"(rod). Whoever this scripture is talking about the reference to "a rod out of the stem" in the context of D&C 113 still implies that someone descended from Christ, even if it is not Joseph Smith. We could look at this in two ways:

1. The "rod/root" is a literal offspring of Christ.
Many LDS and non-LDS Bible scholars agree that Jesus probably was married. Early LDS leaders such as Orson Pratt, Orson Hyde, Brigham Young, and Joseph Fielding Smith believed that, Jesus, who descended through polygamous families from Abraham down & who fulfilled all the law even baptism by immersion, would not have lived and died without being married. In those days it would have gone against the laws and customs of the culture for any Jewish man to not be married by the age of 20. By the time He started His ministry Jesus was in His 30's and therefore could have had plenty of time to marry and father some children. The Bible of course is silent on this subject; which in itself is a good reason to believe He was married. For nowhere in the Bible was He accused by His enemies of ignoring this important Jewish law and tradition. Even though this all makes sense, this kind of information is not perpetuated by the leaders of the Church simply because no one knows for sure. It is mostly educated speculation.

2. The "rod/root" is a spiritual offspring of Christ:
Another way to look at the D&C 113 scripture is to notice that it specifically states that the "rod" and "root" are descendants of Jesse, but does not say anything about being descendants of the "stem"(Christ). When the Isaiah scripture says, "there shall come forth a rod out of the stem of Jesse" it may not be talking about literal offspring. Consider the scripture in Mosiah 5:7:

"And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons and his daughters."

This scripture describes how the "rod"(Joseph Smith) could be "spiritually begotten" of the "stem"(Christ). This is how he could be "a servant in the hands of Christ"(DC 113:12). If this is true then there is no need to worry about whether Jesus had any physical offspring. I tend to favor this explanation over the first one.

In my studies on this subject I found a lot of differing opinions as to the interpretation of these scriptures. Fortunately, our eternal salvation is not dependent on understanding any of this perfectly.