“Then one who had escaped came and told Abram the Hebrew, who was living by the oaks of Mamre the Amorite, brother of Eshcol and of Aner. These were allies of Abram.”
Genesis 14:13 ESV
As you are reading through the Bible, it’s always important to take note of the first mention of things. And this one is a biggie. Genesis 14:13 is the first time the word “Hebrew” is used.
Scholars aren’t in agreement about what it means. The NIV Biblical Theology study Bible suggests it may be associated with the name Eber, first mentioned in 10:21, from whom the Israelites are descended.
The online Encyclopedia Britannica puts a different spin on this. They don’t associate it with the proper name Eber, but with the word for “other side”:
… the term Hebrew almost always occurs in the Hebrew Bible as a name given to the Israelites by other peoples, rather than one used by themselves. For that matter, the origins of the term Hebrew itself are uncertain. It could be derived from the word eber, or ever, a Hebrew word meaning the “other side” and conceivably referring again to Abraham, who crossed into the land of Canaan from the “other side” of the Euphrates or Jordan River.“The Hebrew People” in Britannica.com
The NIV Cultural Backgrounds study Bible suggests that it’s a social status designation, similar to a refugee:
The designation of Abram as a “Hebrew” may reflect a social status more than an ethnic identity. The term is usually used in the Bible to identify Israelites to foreigners (39:14 – 17; Ex 2:11; 1Sa 4:6; Jnh 1:9). As a social status it seems to have referred to dispossessed or disenfranchised peoples. This is the usage of a similar-sounding term throughout a wide range of ancient texts (often transliterated habiru, more accurately, Apiru, referring to various people groups throughout the second millennium BC). At times the label implies an “outsider” status and that the people are unsettled or even lawless renegades. Other times they are refugees or political opponents. In the Amarna texts they sometimes serve as mercenaries. The term cannot be considered as a reference to ethnic Israelites, but it is possible that ethnic Israelites (and here, Abram) are being classified socially as Apiru.
The Britannica article goes on to suggest that the name could be associated with the people referred to as habiru/hapiru in the el-Amarna tablets of the fourteenth century bc. However, from looking at various Biblical commentaries, it seems that conservative scholars disagree.