Abraham was the first Hebrew mentioned in the Bible. He was a Gentile before his call to leave his country. Abraham lived in Chaldea in the city of Ur. "Now the Lord had said unto Abraham, Get thee out of thy country, and from thy kindred, and from thy father's house, unto a land that I will show thee (Genesis 12:1)."
Abraham was a Syrian by birth and is referred to as such in the Bible. Even Jacob, his grandson, is still referred to as a Syrian in Deuteronomy 26:5.
The word Hebrew is first mentioned in Genesis 14:13, where Abraham is called Abram the Hebrew. This word comes from the Hebrew root word "Abar" and means simply "to cross over". Abraham crossed over into the promised land and became the first Hebrew. Since Abraham was a Hebrew, his descendants were also called Hebrews. Strictly speaking all of Abraham's descendants are Hebrews. This would include the descendants of Ishmael, who are the Arabs today. Also, the descendants of Esau, the grandson of Abraham, call Edomites. But by common usage, this name is applied to the nation of Israel only.
Abraham was a Hebrew, but he was not an Israelite, nor a Jew. The first Israelite was Jacob, the grandson of Abraham. His mother named him Jacob, but God changed his name to Israel. The name comes from three fragments of other words. The first is "ish" which means "man". The second is "ra" which means "great". The third is "el" which is an abbreviation for "Elohim" which means God. Thus Israel ("Ish-ra-el") means "the great man of God" or "the child of God" or "the prince of God".
Whereas Abraham was a Hebrew, but not an Israelite nor a Jew, Jacob was both a Hebrew and an Israelite, but not a Jew. The name "Jew" refers strictly speaking to only a part of the nation of Israel. After the reign of King Solomon over the twelve tribes of Israel, his son Rehoboam, caused a civil war in Israel by which the northern ten tribes seceded from the southern two tribes of Judah and Benjamin.
This northern kingdom became known as Israel or Ephriam.
The southern kingdom was called by the name of Judah. Around 600 BC, Nebuchadnezzar conquered the southern kingdom consisting of the two tribes of Judah and Benjamin. He transported a number of them to Babylon. Many of those returned from Babylon to Jerusalem under Nehemiah, Ezra, and Zerubbabel at the conclusion of seventy years of captivity. These captives from the southern kingdom were the first to be called "Jews" while they were still in captivity in Babylon. The first mention in the Bible is in II Kings 16:6,7 and the first point of time that "Jews" are mentioned in Jeremiah 34:9.
Instead of saying Judah, they began to say "Jew". This is a slang word that has been used all these centuries for the nation of Israel. It has really been a fulfillment of a prophecy. Deuteronomy 28:37 says, "And thou shalt become an astonishment, a proverb, and a byword, among all nations whither the Lord shall lead thee." It is true to this day that the descendants of Abraham have been called by the slang word "Jew".
So technically speaking, all of the descendants of Abraham are Hebrews. All of the descendants of Jacob are Israelites. And all of the descendants of Judah are Jews (one tribe of Israel); however, common usage has been such that any member of the nation of Israel is called a Jew
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