The deep south are those states immediately adjacent to the Gulf of Mexico, plus (in some contexts) those adjoining them. A gross generalization would be a swath extending from southeast Texas, across Louisiana, Mississippi, Alabama and Florida. However, culturally Arkansas, Georgia, South Carolina, etc., might be included in the term and possibly even others such as Oklahoma, Tennessee and North Carolina.
Weather and climate wise, we’re dominated by the Gulf of Mexico and interactions with cooler / dryer air coming in from the north / western US. We generally get plenty of rain (often 60 inches / 150cm or more annually), it’s often overcast and almost always humid (Koppen “humid subtropical” climate). Tropical weather such as hurricanes are not at all uncommon.
I’m in central Louisiana and that’s my (somewhat tongue-in-cheek) reference to “nothingness”.
We have at most just a few slight rolling undulations in our topography. With 100 foot tall pine trees commonplace, the elevation change is almost never more than the height of the trees so you can’t see above / beyond anything. Mississippi and Alabama have in places slightly more hilly terrain. Arkansas and Georgia have what might be termed “smaller” (i.e., sub-Appalachian sized) mountains. For example, 1,500 foot elevation change can be found in Arkansas. However, the highest point in Louisiana is the somewhat comically-named Driskill Mountain. At 535 feet, from what I’ve seen of photos it requires a sign in the middle of an apparently flat pine forest to indicate you’ve reached the “summit”. LOL
In Louisiana, there are a handful of distinct landscapes:
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Populated areas (towns)
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Wide open flat commercial farm land typically measured in thousands (if not tens of thousands) of contiguous acres
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Seasonally or perpetually flooded cypress swamps
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Dense, mostly pine, forest. It’s also typical to be heavily undergrown with dense vegetation, vines, etc., to the point where periodic prescribed burns are necessary to keep things in check.
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Coastal delta / marsh
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New Orleans
That last bullet point isn’t a joke. New Orleans is in Louisiana but in many respects is unlike anywhere else in the state. Yes, it’s flat and low (below sea level) but the city itself is actually more reminiscent in some regards of New York than Louisiana. For example, one of the common language accents in New Orleans pronounces the city as “nuh-WAH-luns”, much like a more northeast US accent might. I seem to recall reading somewhere that New York and some of New Orleans have some ancestral overlap, which might explain it.
So, to get back to your question at long last… 
Basically take any landscape and remove all effects of elevation change, then you can imagine most of Louisiana. No (real) hills, no valleys, no cliffs, no waterfalls, no vistas, no sea stacks and a coast line where elevation change is measured in inches per mile (almost).
Way, way, way TMI, I know… 