A blockchain is a ledger: a list of every transaction, kept in order. What makes Bitcoin's version special is how that list is built and protected.
Blocks in a chain
Transactions are grouped into blocks. On average, a new block is added about every ten minutes. Each block contains a header with a few key fields: a timestamp, a summary of all its transactions (the Merkle root), and the hash of the previous block's header. That last field is the "chain". Every block points to the one before it, all the way back to the genesis block, timestamped 3 January 2009.
Why it is hard to change
If someone edits an old transaction, that block's hash changes. The next block no longer points to it, so the link breaks. To hide the edit, the attacker would have to redo the proof of work for that block and every block after it, faster than the rest of the network keeps adding new ones. With today's enormous hash rate, that is practically impossible. This is why each extra confirmation makes a transaction safer.
Append-only and public
New data is only ever added at the end. Nothing is deleted. Anyone can download the full history and check every rule by running a full node. You do not need to trust a company's database. You can verify it yourself.
Who decides which chain is real?
Sometimes two miners find a block at almost the same time, and the chain briefly splits. Nodes follow the valid chain with the most accumulated work. Usually within a block or two, one side wins, and the network returns to consensus.
What it is not
"Blockchain" is often sold as a cure-all. Without proof of work and open verification, a blockchain is just a slow database. In Bitcoin it matters because it lets strangers agree on who owns what without a central authority, and that is what solves double spending.