Blockchains are a means to make an immutable record of transactions on a decentralized database. This makes blockchains a useful place to record important information e.g. of a financial, medical or legal nature.
A blockchain is a public database where any update is added sequentially. Since all information is time-stamped. You can add information in the present, but you cannot edit past information. In this way a blockchain creates an immutable ledger.
The name blockchain means that information added to the ledger comes in discrete bundles called blocks. A block points to the block before it. That way, a chain is created that connects the changes on the ledger from the beginning to the present. The blocks are connected cryptographically. The hash of each block is produced as a function of the hash of the transactions and the hash of the previous block.
A blockchain exists on a distributed network of computers called nodes. Changes to the database happen to all the computers on the network through a secure consensus mechanism. In a traditional centralized database, you just need to hack or compromise one computer and the integrity of all content on that database would be in jeopardy.
Conversely, a blockchain is a decentralized database. Therefore, data on the blockchain remains secure even if a computer in the network is hacked, short circuits or loose connection to the internet.