There are really no "Bitcoins", there are only a very long series of inputs and outputs to various Bitcoin addresses, all recorded on the shared block chain. Inputs (Bitcoins) come in to the system through mining, and then they are traded out via outputs and in via inputs.
The smallest value for an input/output is 1 Satoshi. 1 Bitcoin equals 100,000,000 Satoshi. So a Bitcoin is just a convenient measurement of inputs minus outputs.
When you make a purchase from an address, the client adds up your inputs and outputs at that address, and if you have a positive balance, you can send any portion of it as an output to another address (as long as you have the private key to verify that you own the sending address). It is recorded on the block chain as an input to that receiving address records, and the miners (eventually) confirm that transaction by including it in a block -- each time that happens is 1 confirmation (mining is another whole can of worms).
When you make a purchase that is less than the total number of inputs minus outputs at the address you're spending from, you can receive the difference via an input to either the same address or another, new address, depending on the Bitcoin client used.
Does that make sense? It's all just a shared accounting system.
The smallest value for an input/output is 1 Satoshi. 1 Bitcoin equals 100,000,000 Satoshi. So a Bitcoin is just a convenient measurement of inputs minus outputs.
When you make a purchase from an address, the client adds up your inputs and outputs at that address, and if you have a positive balance, you can send any portion of it as an output to another address (as long as you have the private key to verify that you own the sending address). It is recorded on the block chain as an input to that receiving address records, and the miners (eventually) confirm that transaction by including it in a block -- each time that happens is 1 confirmation (mining is another whole can of worms).
When you make a purchase that is less than the total number of inputs minus outputs at the address you're spending from, you can receive the difference via an input to either the same address or another, new address, depending on the Bitcoin client used.
Does that make sense? It's all just a shared accounting system.
EDIT: Clarified role of block chain.