Is it simply defined by its short word count? Or are there other accepted conventions in flash fiction? If it's just the word count, how short is too short? How long is too long?
I have written flash fiction as short as 50 words and seen submissions in the range described by OneMonkey.
Flash fiction is largely defined by the word count, but doing flash fiction well is more than just getting the right word count. Imagine telling an entire compelling story in 200 words. That's an extreme compression of the rising action, climax, falling action sequence. Because of the compression, flash fiction often shares characteristics with poetry. In poetry each word often has multiple tasks and each phrase and image has multiple layers of meaning. Flash fiction is the same way. Flash fiction doesn't necessarily carry the same emphasis on the lyrical quality of the writing as poetry, though.
Because of the short nature of flash fiction, it is often very well suited to intriguing revelations close to the end of the work. The most compressed part of the piece is usually the falling action, which often is less and less important to a story as the word count decreases.
Flash fiction is primarily determined by its word count. The max word count I've seen for flash fiction is 1000 words but could be as low as 300 words. For it to "count" as flash fiction it has to be a complete story with a beginning, middle, and end and not just an excerpt.
There are other sub-categories of flash fiction though:
Micro fiction - Anywhere from 50-250 word max depending on the site
Drabble - exactly 100 words
69er - Story in exactly 69 words
Nanofiction - A story of exactly 55 words
Twitfiction - A story in 140 characters or less
Zoetrope defines flash as a short piece of between 200-1000 words. That's the only restriction they have on submissions to their flash fiction workshop.