What is the significance of Mount Horeb in the Bible?

TL;DR:

Mount Horeb is where God appeared to Moses and gave him the Ten Commandments. Mount Horeb shows us God’s relationship to His people while looking forward to a future covenant.

Mount Horeb, also known as Mount Sinai, is where God appeared to Moses, giving the Ten Commandments and other laws. Despite the people's failure, God forgave them and renewed the covenant at Horeb. God's presence accompanied the Israelites, eliminating the need for pilgrimage to Horeb. Mount Sinai is referenced in the New Testament to contrast the new covenant of grace that came with Jesus. The new covenant, initiated by Jesus, replaces the old, offering salvation through faith and a transformed heart.

from the old testament

Mount Horeb, also called Mount Sinai and the Mountain of God in the Bible, is where God appeared a number of times. The first mention is in Exodus 3:1 when God appeared to Moses in the burning bush in order to send him to free the Israelites from slavery in Egypt. During that exchange, God promised, "I will be with you, and this shall be the sign for you, that I have sent you: when you have brought the people out of Egypt, you shall serve God on this mountain" (Exodus 3:12). That promise was fulfilled in Exodus 17:6 when the people of Israel arrived at Mount Horeb in need of water. God instructed Moses to strike a rock at the base of the mountain and thereby provided water for His people.
Three months after the Israelites left Egypt, God appeared again before the people on Mount Horeb to call Moses up in order to give him the Ten Commandments and other laws (Exodus 19:1, 11, 20). Unfortunately, the people fashioned a golden calf and worshiped this false god while the One True God met with Moses (Exodus 32). Because God is "merciful and gracious, slow to anger, and abounding in steadfast love and faithfulness" (Exodus 34:6), He forgave the people and rewrote the Law for them on new stone tablets (Exodus 34:1).
It was on Mount Horeb that Moses requested of God, "Please show me your glory" (Exodus 33:18). God responded, "Behold, there is a place by me where you shall stand on the rock, and while my glory passes by I will put you in a cleft of the rock, and I will cover you with my hand until I have passed by. Then I will take away my hand, and you shall see my back, but my face shall not be seen" (Exodus 33:21–23).
Similarly, God also appeared to Elijah on Mount Horeb hundreds of years later in "the sound of a low whisper" (1 Kings 19:12).
When God called the Israelites to set out from Mount Horeb and go to the Promised Land, He promised, "My presence will go with you, and I will give you rest" (Exodus 33:14). Indeed, "the cloud of the LORD was on the tabernacle by day, and fire was in it by night, in the sight of all the house of Israel throughout all their journeys" (Exodus 40:38). Because God's presence traveled with the people, there was no need to revisit, or make pilgrimage to, Mount Horeb.
In Deuteronomy, Moses reminded the people that "the LORD our God made a covenant with us in Horeb. Not with our fathers did the LORD make this covenant, but with us, who are all of us here alive today" (Deuteronomy 5:2–3). Interestingly, the generation who had been adults when God gave the Law and made the covenant on Mount Horeb had all passed away, and it was their descendants to whom Moses spoke. God intended that this new generation take ownership of the covenant and identify with the experience at Mount Horeb even though they had not been there. Near the end of Moses' speech, he said, "the word is very near you. It is in your mouth and in your heart, so that you can do it" (Deuteronomy 30:14).

from the new testament

Although Mount Horeb is not mentioned by name in the New Testament, Mount Sinai, which is the same place is.
In Stephen’s speech before the Sanhedrin, he recounts the story of Moses encountering God at the burning bush, referring to "the wilderness of Mount Sinai" (Acts 7:30, 38).
Paul uses Mount Sinai symbolically in an allegory, contrasting the old covenant of the Law (represented by Mount Sinai) with the new covenant of grace. He says, "Now this Hagar is Mount Sinai in Arabia and corresponds to the present Jerusalem" (Galatians 4:24-25).
Mount Sinai is also referenced in Hebrews 12:18-24, although not by name.

implications for today

God's people were not able to observe the Law on their own, so God promised a new covenant "not like the covenant that I made with their fathers… I will put my law within them, and I will write it on their hearts" (Jeremiah 31:32–33). "I will give you a new heart, and a new spirit I will put within you… I will put my Spirit within you, and cause you to walk in my statutes and be careful to obey my rules" (Ezekiel 36:26–27). This old covenant, reliant on human ability to obey laws, initiated on Mount Horeb, was to be replaced by a new covenant, reliant on God's own Spirit.

Jesus initiated this new covenant through His sinless life, sacrificial death on the cross, and resurrection. During the Last Supper, He said, "This cup that is poured out for you is the new covenant in my blood" (Luke 22:20). While Mount Horeb was the site of many appearances of God and where the old covenant was instituted, it is Mount Calvary where God incarnate—Jesus, God the Son who took on human form—came to institute the new covenant. Just like the new generation of Israelites was supposed to take ownership of the covenant instituted with their ancestors, so too is the invitation to participate in the new covenant open to anyone who humbly submits to the Lord. "Because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved" (Romans 10:9).

understand

Mount Horeb, also known as Mount Sinai, is where God appeared to Moses in the burning bush and later to give the Ten Commandments.
On Mount Horeb God forgave the Israelites after they worshiped the golden calf, renewing His covenant.
Moses requested to see God's glory on Mount Horeb, where God revealed Himself partially. Later, on Mount Horeb, God appeared to Elijah in a whisper.

reflect

How does the story of God's appearances on Mount Horeb challenge your understanding of God's character and relationship with His people?
In what ways do you relate to Moses' desire to see God's glory on Mount Horeb? How does that desire manifest in your own spiritual journey?
Reflect on God's forgiveness and renewal of the covenant at Mount Horeb. What does this teach you about God's mercy and grace in your own life?

engage

Over time, the exact location of Mount Horeb was forgotten. Though its location is somewhat debated, most Christian scholars believe it to be one of the peaks in the Holy Mountain Peaks of Mount Jabal Musa, Mount Catherine, and Mount Ras es-Safsafeh in the southern part of the Sinai Peninsula. There is adequate water supply, appropriate amounts of pasturage, and a wide open plain there that align with the biblical descriptions of Mount Horeb. Plus, those peaks are the right distances from other known locations such as Egypt and Kadesh-barnea. However, Mount Horeb's exact location is still uncertain with some scholars believing it to be in the northern part of the Sinai Peninsula and others believing it to be in Arabia.
Controversy exists regarding the exact location of Mount Horeb/Sinai. How does this uncertainty impact our understanding of biblical events, and how can we reconcile different interpretations?
How does the transition from the old covenant initiated at Mount Horeb to the new covenant through Jesus Christ affect our understanding of God's relationship with humanity?