Exodus 18:1-4 meaning

The chapter begins referring to Jethro, the priest of Midian, Moses' father-in-law. Jethro is also called "Reuel" as seen in Exodus 2:18. The name "Jethro" is first used in Exodus 3:1. He was a Midianite. Midian was a son of Abraham by Keturah (Genesis 25:2). The Midianites lived along the east coast of the Gulf of Aqabah (the north-eastern "rabbit ear" of the Red Sea). 

Jethro is called Moses' father-in-law twelve times in this chapter.

The news about the Israelites exit from Egypt was evidently well-known in many (if not all) parts of the ancient Near East because Jethro had heard of all that God had done for Moses and for Israel His people, how the Lord had brought Israel out of Egypt. 

Apparently, Moses had sent his wife and sons back to Midian at some unknown time before his confrontation with Pharaoh and the plagues. This was probably done to protect them from Pharaoh's possible actions against him and his family. The fact that Jethro, Moses' father-in-law, took Moses' wife Zipporah, after he [Moses] had sent her away provides the setting for what happens in the next section of the chapter.

Verses 3 - 4 identify Moses' sons, their names, and why those names were chosen. Jethro not only "took Zipporah," he also hosted her two sons. The first one was named Gershom, for Moses said, "I have been a sojourner in a foreign land." His birth was mentioned in Exodus 2:22. His name is probably related to a Hebrew verb meaning "to drive out" or "to banish." It speaks of the time when Moses fled Egypt because Pharaoh sought his life (Exodus 2:15).

 The second son is first mentioned here. He was named Eliezer, for he said, "The God of my father was my help, and delivered me from the sword of Pharaoh."  It was mentioned earlier that Moses had more than one son (reference to "sons" in 4:20), but his name was first revealed here. His name means "My God [is a] help[er]." It was probably meant to commemorate a time when Pharaoh threatened to kill him but he managed to escape, though the specific incident in view here is unknown. So, it is apparent that Moses named his sons to commemorate his experiences before and during his encounter with Pharaoh. 

The Hebrew word for "delivered" is also used in vv. 8, 9, and 10, making the LORD's deliverance of Israel a very important topic in the conversation between Jethro and Moses in this passage.