What is the coinbase? I searched the bitcoin wiki and found references to coinbase, but no clear cut explanation of what exactly it is.  I know that miners can tag their coinbases (that is how some sites tell who mined a block).
The term "coinbase" is used to mean many different things. But the two you're probably asking about are:


The "coinbase transaction" is the transaction inside a block that pays the miner his block reward.
Inside the coinbase transaction is a field that is called the "coinbase". It's the generation transaction's equivalent of a scriptsig. Since it doesn't claim any existing outputs, it needs no normal scriptsig. It's basically just a random value that the miner can use as an additional nonce. BIP 34 changes this a bit.