A feeling of anxiety, apprehension or illness.
The sound of this term seems to hark back to earlier rhyming phrases, like hocus-pocus and mumbo-jumbo, with a touch of the jitters thrown in. The meaning is more like the British term - the screaming habdabs.
Heebie and jeebie don't mean anything as independent words and heebie jeebies was coined at a time and place when there was a spate of new nonsense rhyming pairs, called rhyming reduplications, - the bee's knees, etc., i.e. 1920s USA.
The term is widely attributed to William Morgan "Billy" de Beck. The first citation of it in print is certainly in a 1923 cartoon of his, in the 26th October edition of the New York American:
"You dumb ox - why don't you get that stupid look offa your pan - you gimme the heeby jeebys!"
Heebie jeebies caught on quickly and very soon began appearing in many newspapers and works of literature in the USA and, from 1927 onward, the UK; for example, here's an entry from the Van Nuys News, 6th November 1923, just a few days after de Beck's cartoon was published:
"Bill Alton showed up poorly in center field. The boys seemed to have the heebie jeebies."
The lack of any explanation in either of the above citations seems to imply that the term would have been known to the readership of both publications by the time of printing.
The speed of take-up of heebie jeebies, in a similar way to another coinage that is attributed to de Beck - horse feathers, does suggest an origin in the media rather than street slang, which tends to spread more slowly.
The term became part of the language quickly enough for it to begin appearing in advertisements from 1924 onwards, as in this illustration from the Mexia Daily News, October 1924, in an advert for a cold cure.
See other reduplicated phrases.
See other phrases that were coined in the USA.