The blockchain is the public ledger which records all Bitcoin transactions. Miners compete to create each block within the blockchain, the difficulty required to find a block is adjusted every 2016 blocks (about every two weeks), so that a new block should be created approximately every 10 minutes.
When a miner creates a block they choose which of the publicly declared transactions to include in the block. When a transaction first gets included in a block it is said to have one confirmation. Each block builds on the previous block, so each further block will add one further confirmation to the transaction.