A bitcoin is defined by a sequence of digitally signed transactions that began with the bitcoin's creation as a block reward. The owner of a bitcoin transfers it by digitally signing it over to the next owner using a bitcoin transaction, much like endorsing a traditional bank check. A payee can examine each previous transaction to verify the chain of ownership. Unlike traditional check endorsements, bitcoin transactions are irreversible, which eliminates risk of chargeback fraud.
A diagram of a bitcoin transfer
Although it is possible to handle bitcoins individually, it would be unwieldy to require a separate transaction for every bitcoin in a transaction. Transactions are therefore allowed to contain multiple inputs and outputs, allowing bitcoins to be split and combined. Common transactions will have either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and one or two outputs: one for the payment, and one returning the change, if any, to the sender. Any difference between the total input and output amounts of a transaction goes to miners as a transaction fee.