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 usage of a secure cryptographic hash functions. The purpose of that proof is to check if calculations were indeed conducted during creation of a new block.