A bitcoin is a unit of measurement. It's no more meaningful to ask what a bitcoin looks like than to ask what a centimeter (or an inch) looks like.
The global shared ledger of the Bitcoin system, the "block chain", holds transactions. Each transaction contains inputs and outputs. All inputs must be valid outputs of a previous transaction. Inputs and outputs have a size specified in bitcoins (with the base unit being 0.00000001 bitcoin, also known as a "satoshi"). All outputs are labelled with a bitcoin receiving address, which is the hash of a public key. The receiving address was generated by the holder of the corresponding private key, who can spend the corresponding output as the input to a new transaction.
A miner collects unprocessed transactions and attempts to get them accepted into the block chain. By consensus (enforced through software), each block is accepted if accompanied by a valid hash whose value is less than a certain limit. Miners compete against each other to be first to find a suitable hash for a new block, because each block is allowed to include a reward for the miner. The reward is a freshly minted output.
The consensus (enforced through software) is that the block reward halves approximately every 4 years, such that the total bitcoins issued will asymptotically approach a fixed maximum of 21 million. Currently the reward is 25 bitcoins per block.
The threshold for a valid hash adjusts approximately every 10 days to ensure that new blocks are produced approximately every ten minutes. This is expressed as the "difficulty factor", and will rise as more hashing power joins the network.