Imagine that you're working at the office and you're being paid by rolling a dice. Let's start from here and explain basic crypto mining terms and mechanics using this analogy :)
This post was inspired by this reddit entry - user idiot_on_internetuses the mentioned analogy to explain spikes in mining profitability but I think it can be used to describe many other phenomenon in crypto mining.
So, you're working at the office and you're rolling a dice all day. Let's say your boss pays you $3 every time you roll 1,2 or 3.
Hashrate
This value describes how many times you roll the dice every second. It has direct, linear impact on how much you will earn. If you're rolling the dice once every second, your expected income is $1.5 per second. That's because you've got 50% chance to get paid after each roll and 50% from $3 is $1.5
remember you get paid if you roll 1,2,3 - so these are 3 numbers out of 6 = 50%
Now let's say you want to earn more - what do you do? Well, you roll faster :) With 10 rolls a second you're expected income grows 10 times and now is at $15. The rolls per second is your hashrate - the faster your mining equipment can perform calculations (rolls), the more you earn.
Difficulty
Let's say you boss now tells you: OK, change of plans. Now I will pay you only if you roll 1 but I will pay you $9 for that. What does it mean?Well, in terms of how much you earn - nothing. You've got 3 times lower chance for desired outcome, but the profit is 3 times higher when you get it. So when you're mining crypto and the pool (mine) sets higher difficulty for your miner, it doesn't mean that you will earn less. You will get the desired outcome less often but you will earn more for each one. By the way, we call this desired outcome a share.