The word that is translated here as ‘wilderness’ can also mean ‘loneliness’, ‘undeveloped’, or ‘uncivilized’. It implies separation from society, and from civilization. The Latin word used here is ‘deserto’, again meaning alone and unconnected. While we may imagine a barren desert or bald mountain ranges, dense jungles or fields of ice as being the ‘wilderness’, from the Roman perspective, everything outside their borders was the wilderness. Whenever they absorbed a new land into their administrative borders, they would claim to have brought ‘light’ to a new land. They were really very serious about believing that they had the best culture in the world.
For the Greeks and Canaanites, ‘wilderness’ was anywhere outside of urban development, much as it means today. The wilderness is populated by wild beasts, not domesticated ones, and the people who live in the wilderness are often considered underdeveloped.
For the Romans, wilderness was everywhere outside of the boundaries of the Roman Empire. The Roman sense of cultural superiority was legend, and they had a clear idea about the difference between lands that had been illuminated by Rome and those darkened, benighted places that had not. The wilderness is populated by wild beasts, so look to references to foreigners as “wild beasts”.
A corollary to this understanding about Roman cultural superiority was that anyone who was not immediately desirous and pushy about being Roman was clearly insane or otherwise mentally ill. Much of the description of insane or sick people being healed in the Gospels is metaphorical for people being convinced to become good Romans.