Glossary
Coinbase Transaction
The first transaction in every Bitcoin block, paying the block subsidy plus fees to the miner and (optionally) embedding arbitrary message data.
The coinbase transaction has no normal inputs — it creates new coins out of thin air (subject to the protocol's subsidy schedule) and pays them, plus the fees from every other transaction in the block, to whichever address the miner chose.
The coinbase input field also lets miners embed arbitrary data, which is how the famous Bitcoin genesis-block message ("Chancellor on brink of second bailout for banks") was stored. The name is unrelated to the exchange Coinbase, which came later.