Blockchain is a data system where each participant has an identical copy of the information (distributed), but it is not owned by any single member (decentralised). When a change is made, the transaction is timestamped, broadcasted and stored on all computers in the network. Participants reach consensus to the validity of transactions through the use of agreed rules (consensus algorithms) and transactions cannot be altered once verified (immutable). Malicious actions are prevented because the huge computational power required to override data stored in the network.
Cryptography is used to protect the data (secure). Digital signatures/keys are used to ensure participants are authorised to make the transactions, and permissions are used to ensure participants can only access the transactions that they are allowed to see. It reduces the need for trust by improving transparency and accuracy, which in turn reduces the need for intermediaries in transactions.
There are lots of potential ways this technology can be used, from financial services to identity management. They all rely on the decentralised, immutable and secure properties of blockchain.