A blockchain is effectively a database that stores all data related to transactions in a chain of blocks. Usually, new blocks are formed when new transactions take place, and all this happens without a third party.
However, this process works slightly differently on different cryptocurrency protocols. For example, some projects have a public ledger where everyone can see all transactions, and others are more private.
This has attracted a fair bit of attention due to claims that the mining process requires too much power and is bad for the environment — to break the increasingly difficult cryptographic riddles, increasingly powerful GPUs are needed.