Punctuation, like spelling, changes with time. In this case there is no significance that you should be using to interpret the verse, unless you happen to be a student of historical English usage.
The verse you cited is actually not even the original King James Version as published in 1611. In that version the verse reads like this:
And bee not conformed to this world: but be ye transformed by the renuing of your minde, that ye may proue what is that good, that acceptable and perfect will of God.
As you'll notice "be" is spelled "bee", "renewing" in "renuing", "mind" is "minde", "prove" is "proue", and so forth. While the general grammar of the sentence is the same, the version you cited from is actually an updated rendering of the KJV. You probably used what is known as the "Pure Cambridge Edition" that was published circa 1900 — itself based an a 1769 revision. It contains a considerable number of modernized spellings.
You'll also note that between the 1611 edition and the 1900 edition there are actually tons of differences in comma usage. Even the verse you asked about has several differences besides the one you asked about. The point is that orthography changes over time. Words take on different connotations and loose old ones, spelling conventions change, and even punctuation conforms to the demand of popular usage.
Ironically the comma you asked about was an addition in the later KJV revision. That's not to say it is a bad or corrupt version, just that the normal rules of punctuation that helped readers understand the text were not the same over a 100 years ago as they are today. Funnily enough today's usage appears to be more like the original of 400 years ago than the interim period. This is actually more common in the history of languages than I would have expected, but I've run into similar things in Turkish: some modern usages are more similar to 18th century usage than to early 19th century usage. Others of course are radically different.
The KJV is a very good translation that has stood the test of time and even anchored the English language — it is in fact partly due to the King James Bible that English has changed as little as it has over the years. But it would behoove anyone reading it to remember that the translators were working with the language usage of their era(s), not ours. Even for die hard KJV readers it is probably a useful exercise to keep a modern English translation around (such as the ESV which actually hangs onto some of the linguistic heritage of the KJV while substantially reworking it using this century's English) for reference.
P.S. Oxford commas are forever.