Satoshi's original paper on Bitcoin posted November 20138 pages of simple explanations
and a "explain me like I'm 5" post on http://www.reddit.com/r/Bitcoin/comments/1reu69/if_you_have_not_read_satoshi_nakamotos_original/cdmlnfd?context=1" target="_blank">reddit :
Bitcoin is a giant public ledger saying who sent what coins to whom. People have private keys, which they use to sign coin transfers. It's easy to verify signatures. That way only you can give away your coins. But that doesn't prevent you from giving the same coins to multiple people. For that we have the ledger, which puts all the transfers in a particular order that everyone agrees on so you can't pay someone with coins you already spent. Transactions are published on a p2p network. To put them in order, people take sets of transactions, add a random number, and make a cryptographic hash of the whole thing. (Feed data into a hash function and you get an unpredictable number.) If the hash is a low enough number it's a valid block and it becomes part of the blockchain. If it's too high, you change the random number and try again. The block also includes the hash of the previous block, so that puts everything in sequence. It takes a lot of tries to get a low-enough number, so only one block is published every ten minutes or so, by some random person who got lucky. This puts everything in order. It's expensive to do that, so when someone successfully generates a block, they get paid by a special bitcoin transaction that awards them some brand-new coins. That's mining.