i was at the same point when bitcoins peaked my interest. took me few days or a week reading about it to get what it is and how it works, the whole digital crypto-currency concept and how bitcoin operates in my view is brilliant. i'm not sure if i'm capable of explaining it well, i may give it a shot below.
there are 3 ways how one can obtain bitcoins:
- mine it, in essence it is transaction processing, encrypting new transactions and broadcasting it to the network to verify.
- buy on one of exchanges
- trade for goods and services
in order to understand what mining is first you need to understand Bitcoin concept and how it works. for that, you need to know principles how SSL works, private/public keys, what are certificates and how they're generated - it is part of bitcoin security; in order to understand bitcoin networking you need to be familiar how modern p2p networks work, in particular
DHT.
There is a block chain, shared among all peers which is basically chained hashed collection of all past transactions each going back to 50btc rewarded for a solved block. all peers share new blocks added to block-chain and validate them with method called proof-of-work, which is bassically solves a problem how multiple entities can agree on a time-stamp of completed task of a single unit, who or whatever it may be. this proof-of-work concept as far as i understand has been succesfully emplyed by botnets and brute-forsing efforts, when each single worker has its own task and whole network needs to be able to validate it so it wont do double work.
all of this 'magically' blends in very secure transmitting network of simple transactions protected from double-spending, where each node verifies all new blocks solved (meaning added to blockchain with new transactions) - this also done in a very clever way, to verify you need to compare input values that will make same hash that is being passed, bascally verification is doing same work that a miner had to do to successfully solve a block. this maybe better explained on wiki
http://en.wikipedia.org/wiki/Bitcoin..._confirmations - this is what miners do they keep securing and validating new transactions, the ssl part i mentioned before used for generating wallet private/public keys where public key is being wallet address if i'm not mistaken. on top of it all there is a lot of different math that keeps system in balance. please feel free to correct me if i got something wrong or missed anything.
mining explained much better here
https://forum.bitcoin.org/index.php?topic=4132.0
sorry if it doesn't make any sense i'm not all well versed in this myself, i got overall picture how it works, but it doesn't make it any less fascinating.