The area considered Judea under the Roman Empire included the areas (or parts thereof) of the ancient Israelite tribes of Benjamin, Simeon, Judah, Ephraim and Dan. Judea included the cities of Bethany, Bethlehem, Emmaus, Ephraim, Hebron, Jericho and Jerusalem. What is known as the Judean wilderness is located near the Jordan River and the Dead Sea. Under the Romans it was ruled by Herod the Great from 37 to 4 B.C. then by one of his sons, Herod Archelaus, from 4 B.C. to 6 A.D.
A wilderness is commonly thought to be a place absent of trees and totally destitute of inhabitants. In the New Testament, however, the original Greek word (Strong's Concordance #G2048) means a rough and mountainous area that is sparsely settled that does have some forests. The type of land is best used as pasture rather than for tilling. It was in such a rough terrain that John the Baptist preached repentance to the masses (Matthew 3).
The reason why there is a wilderness area near the Jordan is due to an effect called the 'rain shadow.' As weather travels over Judea it encounters the Judean Hills lying east of Jerusalem. As warm, moist air from the Mediterranean rises toward the top of the hills it condenses and drops its moisture just before crossing over the hill tops. The now dryer air continues its journey eastward toward the river. This dry area of Judea receives roughly a quarter of the total amount of rainfall that places like eastern Jerusalem are blessed with.
The book of Luke records how for a period of 40 days and 40 nights Satan the devil, in the wilderness of Judea, tempted Jesus to sin. References to Jesus' temptation are also in Matthew 4 and Mark 1. Luke records three of the devil's temptations. The first temptation was to eat food while Jesus was fasting (Luke 4:3). The second was to be given immediate power over the world (verses 5-7). The third was to test God's love for him (verse 9).