Bitcoin Mining is the process by which new Bitcoins are introduced to the system. By spending compuation power, Bitcoin miners are securing the network and processing transactions.
New transaction records are constantly added to a public ledger of previous Bitcoin transactions. The ledger of previous transactions is referred to as the blockchain because it is a continuous chain of new blocks. The blockchain is used to confirm to the rest of the network that Bitcoin transactions have taken place and are legitimate.
The process of solving complex computational puzzles is referred to as Mining as an analogy to mining other commodities like gold or silver.