PayPal
The only way to send money electronically has always been to rely on a centralized intermediary, say someone like PayPal. And what PayPal does is it keeps track of the amount of money that I have in my account. Say I loaded it from my bank account or I got paid by another PayPal user, and then PayPal lets me send the money I have. Won't let me send more money than I ever have, and will tell somebody else whether they've received money from me. PayPal just keeps this ledger of transactions. So with PayPal, there's one ledger and it's held by a company PayPal.
BitCoin
In the Bitcoin network that ledger is distributed across every participant, so anybody who's connecting to the network has a copy of it on their computer in full, going all the way back to the history of the network when it was first created in 2009. Now, how does new information get added to that ledger? Well, that's this role that miners play. They listen for transaction messages that are validly signed on the network. And they bundle them into what we call a block. They announce this block and they say, "Now, you all take this and add this to your copy of the ledger. We call that ledger a block chain because the miner has just announced a block and that block is mathematically linked to all the blocks in the past. They're chained together like a big long string. What they're doing is providing a public good, they're relaying transactions, validating signatures, putting them into a block, adding that block to the block chain and distributing that to all the people on the network. They're given a reward by the network for performing this public good. And that reward comes in two different ways. One, a Bit Miner is allowed to stick in the ledger of transactions for that ten minutes, one special transaction. And if it says, "I, the miner pay myself 12.5-bit points," and they came from nowhere. This is the only time on the Bitcoin network that anyone is allowed to ever have a transaction that didn't have any inputs, that literally created money out of thin air. At some point, somebody started calling this activity of getting new Bitcoins by providing this public good on the network, mining. It's like digging into the side of a mountain and getting gold.
