In short, a blockchain is a ledger. Imagine a spreadsheet duplicated and stored on thousands of computers in a decentralized network. Then imagine that this network is designed to regularly update this spreadsheet based on user interactions, and in accordance with a well-defined set of rules. This analogy should give you a basic understanding of the blockchain. For a more in-depth explanation see here.
The technology extends far beyond just being a means of data storage. Blockchains can be thought of as a set of protocols - a way of doing things - that is enabled through the use of powerful cryptography and computation. These protocols define exactly how interactions take place and therefore dictate how the system behaves on the whole. These aspects, brought together, constitute an incredible breakthrough and facilitate completely new solutions to previously unsolved problems.