Riffing is not only a musical term rooted in Jazz but also a comedic term.
In common usage the term Jazz has not only several denotations but it also has several connotations: Jazz sometimes denotes an elaboration of something: To take something and elementally mix it up in such a way as to improve upon it.
"I bought an old car and jazzed it up."
"If you want to sell it, you'll need to
jazz it up."
Jazz also has negative connotations:
"I slipped climbing into the truck and
jazzed up my knee."
"The divorce jazzed up my whole life."
Say you had a Jazz quartet; a bass fiddle, a drummer,
a sax, and a guitar. They can take a very old and very familiar tune and jazz it as a group to the point of being practically unrecognizable. Or, they do solo riffs on the melody. This is not a true solo, as, in turns, the musicians increase the volume of what they are playing while the others fade in volume and maintain the basic melody and beat. To riff then, is to touch upon a thing (in this case a melody) and depart from it to the point where it is unrecognizable by itself. Riffing is to touch lightly upon a thing only to depart from it.
Late-night talk show hosts and stand-up comics do topical or celebrity riffs. They may touch lightly upon an issue but quickly depart from it just for comic effect. They do not address or critique the issue or personality in question directly in a sober, mature or scholarly manner; instead they use it as a
springboard to say something silly or irrelevant.
I got an email the other day containing an obviously doctored image of President Obama depicted as a Communist
Witch Doctor. While the image visually riffs on his being of African heritage and a
liberal politician, it does nothing to directly address his national health care policy proposals.