The blockchain is a public ledger that records bitcoin transactions. Every node keeps complete copy of the blockchain. Every block contains hash (validation data) of the previous block thus forming a chain.
When a block — a new group of accepted transactions — is created, it is added to the blockchain and published to all nodes.
In order to be accepted by the rest of the network, a new block must contain a so-called proof-of-work. This proof is asymmetric: easy to verify but extremely hard to generate due to the use of secure cryptographic hash functions. The purpose of that proof is to check if calculations were indeed conducted in the course of creating a new block.