Neither. It assumes evolution. It's about a longstanding controversy within evolutionary theory: the result of a new study that favors one side of the debate.
Can someone please explain the significance in layman's terms?
You need to understand some background first. The earliest "ape-men" are all found only in the continent of Africa. Following these you have creatures that are classified in our genus, "Homo". One of the first, Homo habilis, is still very ape-like and also found only in Africa. Then, however, you get a form called Homo erectus. It has a smaller brain than modern humans (although not by much) and it's skull, especially the face, still looks pretty "apeish," but it's lower body is very similar to that of modern humans.
Homo erectus does something no previous human ancestor did. It migrates beyond Africa. It's found in Africa, Asia (all the way to China and Southeast Asia) and some parts of Europe.
After Home erectus the next universally recognized species is Homo sapiens (i.e. us, modern humans) although in between you have a variety of "archaic sapients" (including Neanderthals but others as well) as distinguished from "anatomically modern" humans.
Now, here's the thing: The first "anatomically modern" humans appear in Africa. Both sides of the debate we're considering agree on this point. So you have modern humans appearing in Africa, but at the same time you already have those Homo erectus, and various "archaic sapients", spread around the world outside of Africa. This was the situation around 700 thousand years ago.
So the question is how did we arrive at the current state of affairs, with modern humans everywhere and everything else extinct. At the extremes there are two possible answers:
The "Out of Africa" hypothesis says that the modern humans migrated from Africa and simply replaced all the archaic forms (killed them, out-competed them, whatever). It denies that the various "archaic" forms in Asia and elsewhere contributed in any significant way to modern populations. Anatomically modern humans only evolved once, and in one place (Africa).
The other extreme position is the "Regional Development" hypothesis. It claims that populations of Homo erecuts and/or archaic sapients in Asia and other places each evolved independently into modern humans.
The "Regional Development" hypothesis was rather quickly moderated to something that might be called "Regional Development with Gene Flow". This position admitted that the migration of modern humans from Africa was significant, but only because the moderns interbred with local populations and thereby introduced modern traits. It's still the local populations that evolved, albeit with some outside help, into the modern form.
Of course various other intermediate views are possible. Then it becomes a matter of emphasis, whether on migrants replacing or local populations evolving.
When this debate first began -- back in the late 80's or early 90's IIRC -- both sides claimed evidence from the fossil record, but generally speaking the DNA evidence was considered to favor "Out of Africa". Advocates of "Regional Development" initially based their case almost completely on details of morphology which they interpreted to link modern populations with archaic or erectus fossils from the same regions.
"Regional Development" advocates also critiqued the DNA evidence for the "Out of Africa" view in various ways, but the significance of the present study is the claim that DNA evidence now provides positive support for Regional Development (with gene flow).
Great summary!