Shem is one of the three sons of Noah. He and Japheth were the ones who went in backwards to cover up their father in his tent without looking at him when he stripped himself naked.
Shem was the progenitor of the Semites and ultimately the Hebrews. The most notable of whom were Abraham, his descendants and especially Jesus Christ. He was the father of Elam, Asshur, Arphaxad, Lud, and Aram.
He would live to be 602 years old, outliving Abraham and into the life of Jacob. There is some evidence that he was the king of Salem, known as Melchizedek (an honorific title: "King of Righteousness"). The evidence is circumstantial, but was accepted by Jewish writers in the first century AD.
His descendants would be superpowers both before and after the Babylonian Empire. The Assyrians who overran Israel, and most of Judah, were descended from Asshur. The Persians were descended from Elam.
The name Shem is general word for "name," which may be derived from the verb form שׂום (shum/sum), which means "put, appoint, make." It can also mean prominent, as in an appointed official. Since Shem was listed first in the lists, it is often assumed that he was the firstborn of the three. However, this prominence was often earned, and such is the case with Shem (see below).
Shem was born to Noah and his wife in the 1558th year of the world, in the 502nd year of the life of his father Noah. This is deduced from the Genealogy of Noah (born after Noah had reached the age of 500) and that of Abram (Arphaxad being born two years after the Great flood when Shem was 100). His older brother was Japheth and they had a younger brother named Ham.
The times were bad, with violence a common problem all over the world. It had been centuries since Enoch had preached of coming disaster, and Noah had begun to warn his neighbors that the time was coming soon. As Shem grew up, his father was probably already gathering materials and perhaps contracting out workers to build the ark.
As soon as he was able, he was helping his father to build what to him was probably the biggest structure he had ever seen. It is not known whether ships were even known in those days. Indications from the scriptures are that the whole world was one large continent. At some point before the flood, Shem became married.
Building the Ark
By the year 1578 of the world, Shem and his brothers probably became the primary construction crew as the ark began to take shape. One can imagine a large tract of land, possibly near the coast, being cleared from the inside outward. Depending on what "gopher" wood was, the forest may have been untouched and hundreds of years old.
Working from plans provided by Yahweh Himself, logs were planed into beams and boards, and a waterproofing coating (translated "pitch," but the word for "covering") was created by burning the scraps and cooking the ashes in the tree's sap. Over the course of about eighty years, the four of them built one of the largest boats of all times.
The last thing to be built was single door large enough for any land animals, in pairs, to enter into the ark. Once that was in place, animals began to arrive from all over. Some were probably unknown to Shem, but most were quite familiar. Perhaps the last to come in were the domesticated animals reserved for sacrifice -- those ritually "clean" animals used for religious and other domestic purposes. Whereas these animals were not yet used for food, it is probable that the milk of the females and the hair of their fleece were valuable commodities of the day.
The Flood and Recovery
When God announced the Great Flood was imminent Shem would have entered the Ark along with his wife, brothers, and parents. He would have endured life in the Ark along with his family for a period lasting over a year. After the flood and the water associated with it had died down he left the Ark and lived on Mount Ararat for some time with his family.
During this time Noah became drunk from wine he had grown and was unknowingly laying in his tent naked. When Shem's brother Ham saw his naked father, he went out and told his brothers. Out of discretion, Shem and Japheth walked in backwards and covered their father. After Noah heard about the incident he blessed Shem and Japheth's ancestors, pronouncing that Ham's son Canaan and his offspring would be enslaved to Shem's offspring.
The 'Religion' of Shem
From what can be gleaned from the text, Shem at least trusted his father Noah as the ark was being made. Noah is noted to have been a 'preacher of righteousness,' and his sons all followed him into the ark. Shem would be the chosen son to bring about a godly progeny after the flood, and would do the right thing in an embarrassing situation for his father some time after the birth of Ham's son Canaan.
However, it is perhaps instructive to note the names of his sons for some insight into his religion.
First listed, and perhaps firstborn, of his sons was Elam (`Olyam), a term that means "eternity." The root for this word is OLIM, which means "hidden." The idea is probably that the ways of God in creation and in time cannot be known apart from direct revelation. Shem was perhaps declaring to the family, in the days immediately after the flood, that the future was in the hands of God.
Later that same year, Asshur was born. The name Asshur means "Blessed," from a root meaning "to step" or "progress." A new world was beginning to bloom and produce fruit. The family did not have to live off the storehouse of food from the ark. God was keeping his promises. Some time in the next year, the second year after the flood a son transcribed as Arphaxad was born. The origin of this name is obscure, but broken into parts it could mean "Light on the ground-breakers," that is, Ur of the Chaldees. In Hebrew the word Ur is a spelling of the root for "light" as found in Genesis 1.
In all likelihood, Arphaxad breaks down to Ar-p-chasad, where the "p" is borrowed by Hamitic (Egyptian) sources. In this scenario, the original name of Shem's third son was likely just "Ur," but the Chasad could have been added based on the breaking of the ground to plant Noah's vineyard. As the vineyard grew, and produced plentiful fruit, Noah celebrated but became intoxicated. With this, the first conflict arose in the new world, resulting in the apparent disinheritance of Ham and his descendants. Consequently, Shem may have named his next son "Lud" which means "strife." Perhaps calling upon God once again, Shem named his fifth son "Aram, meaning "exalted."
At the time of the dispersion from Babel, it seems that Arphaxad and his family ended up in "Ur," most probably founding the city and naming in after Arphaxad (Ur). However, Shem seems to have ended up among cousins of his in the lands of Canaan, his nephew. Years later, a mysterious king, also a priest of El Shaddai (the one true God), met with Abram in the midst of his travels. Since Shem lived 600 years -- 502 years after the flood -- he would have actually outlived Abraham. As the Patriarch of the family, and having lived with Noah and survived the flood, Shem had knowledge of God and His power.
After the flood and Shem's subsequent life and dispersion from Mount Ararat, nothing else is definitely known about his life. It is possible that Shem may have been the High Priest of God during Abraham's time, Melchizedek, due to Shem's outliving of Abraham. Shem died at the age of six hundred and two.
Shem held an important role in the advancement of the promised "seed of the woman" that would come to crush the head of the followers of "the serpent." From the death of godly Abel on, the godly line was found in the descendants of Seth, and that passed through Noah to Shem. Though his siblings and cousins scattered in families, it seems that Shem held to the religion of Noah, preserving it until Abram could be taken from his pagan upbringing to become God's chosen line. Shem was there to bestow blessings in a time of need.
Though several generations removed, his descendent Heber/Eber became the progenitor of the "Hebrew" people. In time, the descendents of one of those Hebrews, by putting his faith in God, earned the right to continue the line of "Hebrews." It may have been that Shem had actually been allowed to keep the language of Noah when everyone else was being made to speak languages so diverse that they had to separate from coworkers. Related languages -- and people -- became known as "Semitic," having been named after Shem.
Sometime during the days of Isaac, and possibly even after the twins Esau and Jacob had been born, Shem died at the age of 600, in the year of the earth 2158. He had lived to see the Great Flood, the fall of Babel and the destruction of Sodom and Gomorrah. He had preserved the true religion and passed it on to not only Abraham but to Job of Uz, a Semitic tribe close to Ur.