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. The blockchain serves to confirm transactions to the rest of the network as having taken place. Bitcoin nodes use the blockchain to distinguish legitimate Bitcoin transactions from attempts to re-spend coins that have already been spent elsewhere.
The primary purpose of mining is to allow Bitcoin nodes to reach a secure, tamper-resistant consensus. Mining is also the mechanism used to introduce Bitcoins into the system: Miners are paid any transaction fees as well as a “subsidy” of newly created coins. This both serves the purpose of disseminating new coins in a decentralized manner as well as motivating people to provide security for the system through mining.
Mining is a term used to describe the process of adding new transactions to a blockchain. The competitive process that verifies and adds new transactions to the blockchain for a cryptocurrency that uses the proof-of-work (PoW) method. The miner that wins the competition is rewarded with some amount of the currency and/or transaction fees.
Mining can also be defined as ‘the process of confirming transactions on a blockchain’ or ‘a group or network that solves complex mathematical puzzles to confirm transactions on a blockchain’. This means that mining is not just about mining blocks, but also about verifying transactions on top of those blocks using cryptographic hash functions and securing blockchains against double spending attacks.