I'm aware of that 'Fringe' means 'not major', 'not mainstream'. I hardly understand how 'fringe' and 'meeting' meet as one vocabulary.
The term is most commonly used, in UK politics at least, to describe meetings that take place at a political party conference that aren't part of the main proceedings. They are usually small, and address a particular special interest. Here are some examples from the Conservative, Labour and Liberal Democrat parties.
"Fringe" means something slightly different than "not major." The non major part of fringe implies "alternative" or "extreme":
These people hold fringe values
They are located on the fringe of the metropolis
There isn't anything in the term that implies "small" other than something else exists that is probably larger. A fringe can be massive — especially when describing the surrounding of a core ideal or place.
Taking these things into account, a "fringe meeting" can mean any of the following:
- A meeting located on the fringe of something else — "We just came back from the fringe meeting."
- A meeting about a topic considered "fringe" — "You can find the strangest beliefs at a fringe meeting."
- A secondary or alternative meeting as opposed to the primary meeting — "The boardroom's rulings resulted in many fringe meetings."
- A meeting about extreme alternatives or paths differing from the current plan — "We need to host a fringe meeting to spice up our portfolio."
All of this being said, the fourth example is most likely the closest to the usage you are hearing. One of the casualties of buzzword lingo is that "fringe" is a neat sounding way to say "out-of-the-box". The latter is now a codified cliche; the former is just its euphemism.
If you are not in a business setting, than the second option above is more likely. "Fringe beliefs" often refer to topics popular outside of the typical corpus of human behavior. NGrams somewhat interestingly shows a spike in usage during the 60-70s. My history of philosophy is a little rusty, but I believe that this was during the rise of postmodernism and the tail 60s counterculture movement.
Fringe is the decorative edging on a piece of material (like curtains) - hence something slightly fun and frivolous on the edge of the main meeting is a fringe.
The Edinburgh Fringe (comedy festival) was an underground fun thing alongside the larger, official and more staid Royal Edinburgh Tattoo - the fringe is of course now the bigger media event!