Basically in simple terms, think you're playing the lotto and buy one ticket. You have a chance of winning with just one ticket, but your odds are very low, and they increase if you play with more tickets. (the big mining pools and farms are playing with millions of tickets).
So the number of Best Shares that Apollo shows contains only the Best Shares for my latest attempt (last 10 min) or ALL historical Best Shares since I started mining?
Now think if they pull the winning numbers first, ( the difference is instead of only 6 numbers the numbers are thousands) and we need to buy random tickets looking for the right combination of numbers before anybody else does. Your one ticket hits 1 number, not enough to win, but that is your best ticket, now you buy another, and you hit 3 numbers, this is still not enough to win, but this is your new best. Every new block @10 mins is a new lotto drawing, your old best number from another block means nothing toward the new block other than a way to show how close you had come to winning. The lower your hash rate is like only buying one ticket compared to the mega farms/pool buying millions of tickets every 10 minutes or for every new block.
When Apollo shows 13B Best Shares, does it mean that I managed to pull 13B winning tickets, that I managed to FIND a Valid Block at the current network difficulty level BUT did it too late?
The winning combination is @the new difficulty number (the winning lotto numbers). Now it's set up to average a block/winner every 10 mins, so if there is a winner faster the difficulty amount of numbers increase to make it harder to find the right numbers and if it goes longer than 10 min the difficulty amount of numbers goes down.
This is clear.