“Jargon,” adopted from French in the 14th century, originally meant “unintelligible talk, gibberish; chattering, jabbering.” It wryly took on its current meaning, “phraseology peculiar to a sect or profession,” in the 1650s due to the fact that such speech was unintelligible to outsiders.
Incidentally, the unintelligible sense of “jargon” also arose around the same time as the word “jabber,” which is from the Old English word jablen which meant more or less the same thing. (Other Old English variations included javeren, jaberen, chaveren, and jawin.)
“Jabber” gave rise to “gibberish” around the 1550s as an adaptation of “jibber-jabber.” In the 17th century, “gibberish” was used pejoratively to refer to the language of gypsies and rogues.
And as you probably know, Lewis Carroll capitalized on the meaning of the word “jabber” in his nonsense-based epic-style poem “Jabberwocky,” which first appeared in Through the Looking-Glass, and What Alice Found There(the sequel to Alice’s Adventures in Wonderland) in 1871.
Semi-related fun fact: In the early 2000s there are several tongue-in-cheek instances (example) of the word “jargonaut” used to refer to someone who uses too much jargon, the latter half of which is of course a punny callback to the Argonauts (sailors on the Argo) of Greek mythology who quested for the Golden Fleece.