Like the other definition suggests, Middle America denotes the region of the USA which lies between the two coasts. The term is largely synonymous on the level of meaning with broader uses of "Midwest."
The two terms, however, differ in their connotations. While "Midwest" is a term whose etymology is unclear (what, exactly, is the Midwest in the middle of?), "Middle America" marks the Midwest by contrasting it with the two edges on the east and west. "Middle America," then, always marks its signified term through contrast with the unmarked coasts.
The effect of this contrast is to insult. The term is almost always derogatory, as the other definition shows. "Middle America" is seen as secondary in importance to the coasts, unimportant and not worth knowing, and this attitude is justified through various caricatures: those from "Middle America" are provincial and unsophisticated, etc.
In short: "Middle America" is a perjorative term for the "Midwest."
"Peoria always strikes me as quintessential Middle America: small and unexciting."