Blockchain Basics
sitepen.com
sitepen.com
Watch the video, play with the examples and suddenly everything will make sense.
Although I'm more curious about the mining process and how public/private keys are used.
Public key crypto is used to confirm that the coins can move from one account to another, or to be more precise from one output to another input. (there are no accounts in Bitcoin, that's just an illusion)
Of course a miner could just use a different, bigger value but then the block would not be accepted by anyone else and be basically worthless.
The rules are there because everyone is using the same client or bug to bug compatible alternative.