Ok, so now you have you GPU humming away and you want to know what the frack it is doing.
My assumption is that I will have no idea how this is working in anything more than the broadest terms, so that is what I have focused on learning. This is a bit vague, but it should convey the basic idea.
Basically think of it like this:
There is a big box full of money.
Whoever opens the box gets to say who the money belongs to.
When the box is closed, none of the money can be reassigned.
Now, obviously there is a problem, to transfer money you have to open the box, but if the box is open the monies can be stolen.
Solution: Make it so that the box has to be opened by a bunch of people working together.
Why don’t all the people just steal the money? Well, if they aren’t all trying to open for the same result, they can’t combine their power. Turns out it is hard to get thieves to share the pot. Plus, there is a good chance someone would notice that all their coins are gone, and then a lack of confidence in the coins would make them worthless. (In this case fiat works to the coins advantage)
Now, over time, people get better at opening the boxes. (GPUs get more powerful, dedicated FPGAs get produced, etc) As a result the box makes itself get harder to open, so that no one person can open it. Keep in mind that it is important that the box isn’t too hard to open, or no one will be able to get their money out.
Of course, there has to be a reason for people to open the box other than stealing the money inside, and that is where the reward comes in. Upon opening the box, whoever opened it gets a reward that is composed of transaction fees and (in some cases) newly generated coins.
Note that I said whoever (singular) opens the box gets the reward. For now you should just assume that it is split up amongst the group of people who worked to get the box open. What I said about it being a group, actually ends up basically being true, even though it is sort of a lie