Genesis 11:10-15 meaning

The genealogy of Shem serves to introduce his descendent, Abraham. Accordingly the historical record now narrows from the scope of the entire human race to one branch of humanity, those descended from Shem, or  the Semites. It narrows further to one man, Abram, who becomes the head of the Hebrew nation.

In Genesis 11:10-26 the family lineage is noted, from Shem to Abraham, covering ten generations. The generations of Shem provide the beginning of the history of God's chosen people. God chooses a particular people through which to bless and bring deliverance to the entire human race.

The Genesis narrative now transitions from general history to Hebrew history, and the beginning of the patriarchal era. The lineage of Shem, which culminates in Abraham, is placed immediately following Babel's inhabitants' failed attempt at making a name for themselves.  This shows a contrast, that a truly great name comes by God's grace and obedience to Him.

Arphaxad is the firstborn of Shem. He was born two years after the flood (v 10).

Shem fathered Arphaxad at one hundred years old and then lives five hundred more years, which gives him a total life span of 600 hundred years, considerably shorter lifespan than Noah (950 years, Genesis 9:29). Abraham was also 100 years when his son, Isaac, was born (Genesis 21:5). Ishmael was born when Abraham was 86 years old (Genesis 16:16). What should be noted is the dwindling life spans of the patriarchs following the flood. Arphaxad's life (438 years) is only two-thirds of his father Shem (600 years), and Peleg's life (239 years) is about half of his father Eber (464 years). In the early patriarchs, having children at great ages is common. By the time of Abraham, being one hundred is considered being past child bearing age (Genesis 17:17). Abraham's grandfather Nahor lives only 138 years which is less than Abraham's 175 years.

Eber, the fourth generation, is the last of the patriarchal ancestors to live more than four centuries. The lifespans of the six generations listed after Eber are about half the length of the first four generations after Noah. By the time of King David (around 1000 BC), fourteen generations after Abraham (Matt 1:17), the expected life span is seventy years, roughly what it is today in developed countries (Psalm 90:10).