The name Horeb in the Bible
Horeb (a.k.a. Sinai, and the Mountain of God) is the mountain where Moses fasts for two times forty days back to back, as he receives the Law (Exodus 3:1). Later Elijah the Tishbite also spends forty days fasting on Horeb (1 Kings 19:8), after which he has his famous conversation with God in the cave (19:9-18).
Etymology of the name Horeb
The name Horeb comes from the root group חרב (hareb I & II):
For a meaning of the name Horeb, Jones' Dictionary of Old Testament Proper Names reads Arid. NOBSE Study Bible Name List reads Desert.
Another name that means Dry Place is Zion, which is also a mountain.