Best place to ask this is actually in the flash groups - Prospero gave me a brilliant answer to the same question, a brilliant answer that, regrettably, made no long-term impact so that I cannot remember it.
However, he did quote Hemingway's astonishing flash in six words:
"For sale, baby shoes, never worn."
The gist is that it is a complete story with characters, beginning, middle and end. The airy-fairy bit is the implication that it should be bigger than the sum of its words (eg: the Hemingway suggests so many levels of human emotion and traits to the character writing that it punches far above its wordcount).
That said, it is essentially wrting to a wordcount. Typical limit is are less than 1000 words... but a story of 1001 words is still a flash to me! The thing is, the effort of constraining a full storyline to fit the space usually results in tighter, better, more expressive writing.
Other interesting sub-definitions:
A Dribble (a flash of exactly 50 words)
A Drabble (a flash of exactly 100 words - from the game in Monty Python's Bok [sic] that decided 100 words was the shortest possible length to contain a novel)
The best way to learn is to actually have a go...
For example, I am running very low on entries for this week's challenge in Flash II:
http://www.writewords.org.uk/groups/103_337718.asp
It's only 136 words so shouldn't take you long.
Cheers,
Gaius
<Added>PS: It's also a good way to get feedback from a wider reading public so as to escape the hideous black-box of rejections from agents etc. If you get a story on somewhere like
http://www.everydayfiction.com not only do you get the excellent input from their excellent readers and editors, regardless of whether or not they accept you, but you also get an insight into how your writing actually comes across from the comments and, of course, the satisfaction of seeing your work out there. Recommended.