Blockchain was invented to solve one particular problem: distributed consensus on a sequence of transactions, where the choice of which transaction to include from a set of conflicting transactions is irrelevant. The latter property here is key to understanding where blockchain is useful. It was created to solve the "double spend problem", ie. two transitions that spend the same coin but send it to different recipien…
The word Blockchain is so overloaded, people forget you can build a "blockchain" in 50 lines of code if not less. "Mining" new blocks is added on top of that, it's not a hard requirement - you can just create new blocks and link them up. You can choose to "mine" on CPU (slow) or on the GPU, if you want "mining" at all. You can then choose to persist it (file or sql or whatever) or only run it in memory. After that you can get into the concept of ledgers and currencies, and after that into making it distributed via some gossip-y protocols.
So a cleaner definition of a block chain would be, a tamper-proof daisy-chained data structure, similar to a linked list. All the stuff about ledgers, currencies, mining and consensus are separate concerns, stacked on top of a blockchain.
Also checkout: Merkle trees, linked lists, Chain of Responsibility.
Anyone agree/disagree?