Mining is the process of adding transaction records to Bitcoin's public ledger of past transactions (and a "mining rig" is a colloquial metaphor for a single computer system that performs the necessary computations for "mining". This ledger of past transactions is called the block chain as it is a chain of blocks.

Where do bitcoins come from? With paper money, a government decides when to print and distribute money. Bitcoin doesn't have a central government.

With Bitcoin, miners use special software to solve math problems and are issued a certain number of bitcoins in exchange. This provides a smart way to issue the currency and also creates an incentive for more people to mine.

(source: bitcoinmining.com)