A (potentially distributed) datastructure of some kind, which resembles a linked-list, and ensures its integrity using some sort of cryptographic hash of the previous link such that changing any link but the most recent invalidates the whole chain. Literally -- a chain of (data) blocks.

A non-engineering description of a "blockchain" should be considered to be misleading.

edit - also, I'd take cryptocurrencies more seriously if they could stay out of the headlines for a while