IIRC, the term came from slang for a heroin addict (a jones). If you are jonesing for something, then you are addicted to it, and are needing another fix.

I first heard the term "jonesing" on a recent NPR program. In the inner city, so to speak, jonesing is the art of insults. It is termed as such for unknown reasons but it is very popular in the stereotypical urban jungle (or perhaps only in Washington, D.C.)

Hearing of this "sport" reminded me of a time on the playground at my elementary/middle school, when the two "tough guys" of the class (the complete opposite of the social scale that I was on) decided to have an insult war to see whom was the toughest, which would ultimately decide which one would receive the reverence of the females that particular day. It was both awe inspiring and a tad revolting for me at that young age; I don't remember having been exposed to that amount of vulgarity prior to that day. (Had I had the foresight to see how bad my mouth is at the present day, I would have eaten a box of soap bars).

American slang meaning "desperately waiting for".

Example of the use of the word "Jonesing", from a Beastie Boys song, "Shake your rump"...

now Randy listen I rock a house party at the drop of a hat
I beat a biter down with an aluminum bat
A lot of people they be Jonesin' just to hear me rock the mic
They'll be starin' at the radio staying up all night...