"Bozart" was Mencken's funny way of writing the French term beaux arts, and by "Sahara" he meant "desert." So the phrase is saying that the Deep South had become a desert as far as culture was concerned. Nothing of any importance was being produced in literature, music, or art. This may have been true when Mencken wrote his essay many years ago, but since that time a lot of good art has come out of the South. The jazz that was created in the South has influenced music all over the world. There have been many outstanding poets and fiction writers emerging from the South, of whom William Faulkner is perhaps the outstanding example. The South took a devastating beating in the Civil War and needed some time to recover the artistic prestige it had once enjoyed. See the first reference link below for discussion of Mencken's essay "Sahara of the Bozart."
Part of this phrase by H.L. Mencken ("Sahara of the Bozart") is easy to interpret and part of it is hard to interpret.
The easy part is the word "Sahara." The Sahara is one of the most arid deserts on this planet, located in the heart of Africa. Just as in geography, then, Mencken means Sahara to mean a "vast, arid desert."
It is the term "Bozart" that might cause a problem for a reader not very familiar with H.L. Menken. Keep in mind that the French term beaux arts means (basically) "the study of artwork" or "the study of art." Being sarcastic a bit, Menken created the term "Bozart" to mean the same thing. It his Menken's little nickname for it.
Now let's take the term as a whole and the "Sahara of the Bozart" suddenly means that the South is the "desert of the art world." H.L. Menken's point is that the South produced nothing effective in regards to artistic talent: not art, not literature, not music.
I take offense at H.L. Menken; however, I realize that his words were written a long, long, long time ago. What about bluegrass? What about gospel? What about jazz? What about Faulkner? [Humph!] I can also understand how much war has devastated the American South. Even NOW people down here are proudly flying confederate flags. We obviously have not recovered.