The use of the term "desert places" in Robert Frost's poem of that title uses the term in the classical sense in which the term desert meant an area that was uninhabited, or what would, in modern English, be termed "wilderness". Thus in the Latin Vulgate Bible, the phrase "vox clamantis in deserto", referring to John the Baptist, means "a voice crying out in the wilderness." Because in the ancient Near East, areas with water tended to be inhabited and arid areas with no access to water empty of people, the most common form of wildernesses were very arid areas, and thus the gradual association of "desert" with aridity.
In Frost's poem the ultimate external desert place is outer space, because it is completely uninhabitated by humans:
They cannot scare me with their empty spaces
Between stars--on stars where no human race is.
The final two lines make the point, though, that loneliness is not merely an external but also an internal condition:
I have it in me so much nearer home
To scare myself with my own desert places.