Who was Shem (Gen 10:21-31) and why was he important? What about Eber (10:21, 24-25)?

As to his location and those of his descendants, see the table above. His name is the source of the word “Semite.” This implies that not just Hebrews, but all the Arab tribes, as well as Syrians, probably the Babylonian and Assyrian peasantry, and a number of others, were considered Semitic. But among those who were not deemed Semitic included the Canaanites (most importantly), the Egyptians, and Nimrod, the founder of Babylonia if not many of the people. Note that not all the people who were purportedly descended from Shem spoke a language of the Semitic language family; some spoke an Indo-European language. That the connections are close enough is interesting. As to Eber, it was he after whom the Hebrews were named.