So a mining expert may have to correct me, but my understanding is that it's a difficulty target set by the pool. You beat that target and "share" the hash with the pool to verify your hash rate. 

At either extreme, the pool would be looking at every single hash your miner submits (too much network traffic), or it would never submit a hash until your miner beats the network difficulty. For pools with constant payouts, you need that to figure out your miner's contribution to the total hashrate. 

For solo mining, I don't think it really does much other than let you compute and see your hash rate. On a Bitaxe, you'll see that share difficulty target in the logs. The pool should adjust that number so you submit something (this is the "accepted" share) every few seconds. 

The difficulty number value matters, also. If you're beating a difficulty of 10,000 every 5 seconds, that carries more weight than beating 1,000 every 5 seconds. To do that must mean you have more hashrate, so a pool like Ocean would pay you more. 

Again, I could be grossly misunderstanding or leaving out some crucial piece of that. I learned this with the Nerdminer and Bitaxe, not big boy miners.