A largely useless distributed data storage system unless you're a criminal.
A blockchain is a type of database, and the participants in that database are other computer users.
It's designed to be auditable as a historical record of data (e.g., payments) that is received, processed, saved, and viewable according to set rules.
There are specific rules about how to put data into the database to retain its consistency, but no centralized authority empowered to make changes about the immutable rules unless every user agrees.
Unlike a centralized database, a blockchain is different in that no single computer in the network decides what all other participants see.
The ideological basis for the blockchain is that other participants in a given system of exchange, such as a marketplace, cannot be trusted (such as a market). The blockchain is intended to resolve this fundamental distrust by making everything transparent.