Question: "What is the significance of the fact there were giants in those days (Genesis 6:4)?"
Answer: Genesis 6 records the expansion of the human race and its descent into further corruption. The writer records that there were “giants on the earth in those days” (Genesis 6:4, NKJV) and offers a brief explanation of how that came to be.
As humanity multiplied and began to be numerous on the earth (Genesis 6:1), the “sons of God” took wives (Genesis 6:2), and they began to increase. In light of the rapid multiplication of humanity and its evil, God limited the human lifespan to one-hundred, twenty years (Genesis 6:3). Prior to that time, people lived a very long time—even up to around nine hundred years (see Genesis 5). Though lifespans were decreasing on their own, God intervened to limit them greatly. Despite this significant limitation, there were giants (Hebrew, Nephilim) in those days—in the days of Noah. These were mighty men of renown and were apparently the products of relationships between the “sons of God” and the “daughters of men” (Genesis 6:4).
The giants in those days were extraordinary, leading some to suppose that the “sons of God” in Genesis 6:2 and Genesis 6:4 are fallen angels and not merely regular people. In that theory, these fallen angels took on physical form and procreated with women. The demon-human hybrid DNA resulted in giant size and, apparently, enhanced physical abilities. There are three objections to this theory: First, there is nothing in the text that suggests the “sons of God” are angels. While the phrase can be used of angels (as it is apparently in Job 1:6, 2:1, and 38:7), it is also regularly used of people (e.g., Matthew 5:9 and Luke 20:36). Second, there is no indication that angels are physiologically compatible with women and can procreate with them (unless this is the only instance). Third, the theological implications are significant enough that one might expect some further explanation. Instead, we only see the offspring referred to as “giants” (Nephilim) and mighty, but nothing beyond that.
Others have suggested that the sons of God might be people possessed by demonic beings. As in the other view, the phrase sons of God would still refer to fallen angels. While this view would resolve the physiological implications, there is nothing in the text that would suggest this possibility.
A third view is that there were giants in those days simply because humanity hadn’t been fully genetically corrupted—everyone was big and tall and mighty—and God intervenes to shorten human lifespans. This theory takes the biblical account at face value, that these sons of God were simply men. In any case, there were giants in the land at this time before the flood and “afterward” (Genesis 6:4). There were still giants during the time of Israel’s conquest of Canaan (Numbers 13:33) and David’s time (1 Samuel 17:4–7). If these Nephilim were superhumans resulting from demonic and human cohabitation, it seems they would have died in the flood (Genesis 7:21–23). The fact that they were still around after the flood is either evidence that the fallen angels performed the same act again at some point after the flood, or it is another indicator in support of the third view that these giants on the earth from time to time were exceptional, but not superhuman.
Whatever the case, Genesis 6:4 states that there were giants in the land in those days. The passage does not explicitly say how these giants came to be. It is best to not be dogmatic on an issue that the Bible says so little about and that is not theologically significant in the grand scheme of things.