Eliezer was a son of Moses and Zipporah, and the brother to Gershom.
He was born in the land of Midian, which in ancient times referred to a place near Israel but on the east side of the Jordan River. He was the grandson of Jethro, who was a priest in Midian.
The name Eliezer is often translated as "God is helper." The name Gershom is similar to the Hebrew word for "foreigner" or "stranger." The reasons for the names are explained in Exodus 18:3-4 (NIV translation):
One son was named Gershom, for Moses said, "I have become an alien in a foreign land"; and the other was named Eliezer, for he said, "My father's God was my helper; he saved me from the sword of Pharaoh."
Next person in the Bible: Elihu