As it turns out, not very important at all. Apparently the BOM does not contain a single mention of “giants” or use of the term “Nephilim” (please correct me if I'm wrong). The Book of Moses (see below) contains only two references to “giants” and no references to Nephilim.
“There is a prevailing doctrine in the Christian world that these sons of God were heavenly beings who came down and married the daughters of men and thus came a superior race on the earth, the result bringing the displeasure of the Lord. This foolish notion is the result of lack of proper information, and because the correct information is not found in the Book of Genesis Christian peoples have been led astray. The correct information regarding these unions is revealed in the inspired interpretation given to the Prophet Joseph Smith in the Book of Moses. Without doubt when this scripture was first written, it was perfectly clear, but scribes and translators in the course of time, not having divine inspiration, changed the meaning to conform to their incorrect understanding. These verses in the Prophet's revision give us a correct meaning, and from them we learn why the Lord was angry with the people and decreed to shorten the span of life and to bring upon the world the flood of purification.”
In other words: Nephilim are nonsense. Here are the passages from Moses 8:13-18 that are the re-interpretation of Genesis 6:4:
“13 And Noah and his sons hearkened unto the Lord, and gave heed, and they were called the sons of God.
14 And when these men began to multiply on the face of the earth, and daughters were born unto them, the sons of men saw that those daughters were fair, and they took them wives, even as they chose.
15 And the Lord said unto Noah: The daughters of thy sons have sold themselves; for behold mine anger is kindled against the sons of men, for they will not hearken to my voice.
16 And it came to pass that Noah prophesied, and taught the things of God, even as it was in the beginning.
17 And the Lord said unto Noah: My Spirit shall not always strive with man, for he shall know that all flesh shall die; yet his days shall be an hundred and twenty years; and if men do not repent, I will send in the floods upon them.
18 And in those days there were giants on the earth, and they sought Noah to take away his life; but the Lord was with Noah, and the power of the Lord was upon him.”
Giants are only mentioned in the Book of Moses in one other place that showed up in my search:
“And the giants of the land, also, stood afar off; and there went forth a curse upon all people that fought against God;” (Moses 7:15)
That appears to be it for the giants.
The apparent unimportance of giants in the Book of Moses and the BOM contrasts starkly with the Nephilim-centric view of the world espoused by the Christian fringe, where matings between fallen angels and humans brought on the Flood, provided a rationale for genocide in Canaan, threatened the birth of the Messiah, and continue to endanger humanity today. It is difficult to see how both of these accounts – one in which there is no such thing as a human-angel hybrid (BOM) and another in which there’s a Nephilim lurking behind every rock – could be reconciled. As you might guess, this discrepancy is not lost on the Nephilim enthusiasts.
As far as I can tell, the Nephilim enthusiasts have developed two explanations remedying the absence of the Nephilim in the BOM and the Book of Moses. These may not be mutually exclusive:
- The Nephites (one of the groups of settlers of ancient America) of the BOM actually are the Nephilim. This claim (here is one example) seems to rest on the similarity between the words “Nephite” and “Nephilim.” Here is Fritz Zimmerman’s take on it. This idea seems favorable to those who want to attribute a biblical origin to the existence of "giant" skeletons in the New World.
- The angel that appeared to Joseph Smith to reveal the plates containing the text of the BOM was actually a Nephilim. In other words, the BOM was indeed inspired, but it was inspired by a fallen angel rather than an angel of the Lord. This position is articulated in this video by someone named Penny:
“There is a direct connection between the Nephilim, the fallen angels, and Joseph Smith. I believe that it was a fallen angel that appeared as an angel of light to Joseph Smith and this whole Mormonism thing and the beliefs that they have . . . Mormonism basically suggests that you can be a god, which is the lie, I mean that’s the lie that the serpent told Eve in the Garden of Eden. . . . So, um, if you’re Mormon and you’re watching this, please do not be offended, um, but please wake up and recognize what’s really going on here – that all of your beliefs are based on a lie.”
Here is an account that seems to blend the two.
Finally, it is interesting to note that the BOM publication date of 1830 falls just before the 100-year time period when discoveries of “giant” skeletons were most frequently reported from eastern North America (~1840-1940). If you believe that those BOM texts are inspired, time period perhaps makes no difference. If you believe they are not inspired, however, the cultural context of their production becomes relevant.