Now it is time for our verse break down:
Genesis 11:10
These are the generations of Shem: Shem was an hundred years old, and begat Arphaxad two years after the flood:
The Tower of Babel incident of Genesis 11:1–9 is tied to the genealogical table of chapter 10 by the reference to Nimrod, a grandson of Noah’s son Ham, at 10:8–12.
The Babel narrative serves to explain what has preceded and what will follow by connecting the development of distinct nations and cultures to the corresponding distribution of languages.
Following this story, the author resumes the account of the line of Noah’s son Shem. The list in Genesis 11 shows that God’s earlier promise in 3:15—that Eve’s “seed” would bruise the head of the serpent, an allusion to Christ’s victory on the cross—ultimately could not be stopped by the chaos following Babel.
Even though Noah’s descendants are scattered and divided, God’s purpose to redeem His creation through a chosen line is not compromised. This verse begins a genealogy that will directly link Noah's son Shem with Abram, whom God will re-name Abraham (Genesis 17:5).
This sets up the origins of the people of Israel. Unlike the broad, nation-spanning genealogies in chapter 10, this passage tracks a straight line from each man to one of his sons to the next in the line.
This description begins with Shem. Of the three sons of Noah, Shem is the one who is overtly blessed by God (Genesis 9:26). We are told here that Shem fathered Arpachshad two years after the flood when he was 100 years old.
This is the last mention of the flood in Genesis, marking the beginning of a new era. The birth of Arpachshad so quickly after God's command to multiply and fill the earth shows that Shem was living in obedience.
Genesis 11:11
And Shem lived after he begat Arphaxad five hundred years, and begat sons and daughters.
The present genealogy, moreover, being that of Shem, also serves as an adept literary-theological transition to the next thematic “half” of Genesis. The expectation is thus laid that the present genealogy of Shem will likewise be followed by a narrative episode involving the making of a shem (“name”) for a man.
The previous verse began this genealogy linking Shem to Abraham and the Israelites. Shem fathered Arpachshad two years after the flood when Shem was 100 years old. This verse now establishes the pattern for the rest of the genealogy, revealing how long Shem lived after the birth of the next in the line.
Putting the two ages together, Shem lived to be 600 years old, allowing him many years to have other sons and daughters as humanity set about refilling the earth with people. Verse 10 was the last mention of the flood found in Genesis, setting this passage up as a milestone. In the same vein, this genealogy does not focus on phrases such as "and then he died," as did the genealogy of chapter 5.
Genesis 11:12
And Arphaxad lived five and thirty years, and begat Salah:
Observe here, That nothing is left upon record concerning those of this line, but their names and ages; the Holy Ghost seeming to hasten thro' them to the story of Abraham. How little do we know of those that are gone before us in this world, even those that lived in the same places where we live!
Or indeed of those who are our contemporaries, but in distant places. That there was an observable gradual decrease in the years of their lives. Shem reached to 600 years, which yet fell short of the age of the patriarchs before the flood; the three next came short of 500.
The line from Noah to Abraham follows through Shem to Arpachshad and now to Shelah. This is a noteworthy point in Genesis due to the age of Arpachshad when he fathers Shelah: "only" 35 years old. This is a drastic reduction in the age of having children when compared to the pre-flood era (Genesis 5).