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. 

 Some more sats for your time.

Thank you. 

 Oh, no problem, thanks. A tree fell and knocked out our neighborhood power, so you gave me something to do besides lie here and sweat. 😂 🥵 

 Put another way, if whistles are "shares"...

The rules: You have 10 dice. Blow a whistle if you get a total roll value over 40. If you roll 60, you get pizza and ice cream.

Bob can roll the dice REALLY fast. He's blowing his whistle every 2 seconds. We get sick of this, so we change the rules. We tell him he can only blow it if he rolls over 50. This shuts Bob up a little. We know that he's doing his thing, though, rolling his 50+ occasionally.

Alice only has one arm, and it barely works. She hasn't blown her whistle in hours. We change her rules so that she blows the whistle on anything over 15. Now we can see (and hear) that Alice is actually doing something over there. 

Alice is now blowing her whistle about as often as Bob. Bob does get treats all the time, though, because he's rolling like crazy. Eventually, Alice also rolls a 60 with her busted arm and gets her pizza and ice cream.