Imagine if you had a key, and a pile of lockable boxes that only your key will open. Anybody can grab a box + leave a message for you in that box. If you're not in the room, somebody who is in the room will take the box to you. The person who brings you the message can't read it because they don't have your key to open the box. You sometimes bring boxes to other folks too, as you move around different rooms.
A blockchain is the rooms and the people. The boxes + keys are the encryption method (typically asymmetric hashing) that keeps the messages in the blockchain safe.
For Bitcoin, imagine that the boxes are really hard to close, and that it costs money to get boxes. The only people who get to make brand new boxes (which they can then sell) are the people who put forth the effort to close the existing boxes. The messages inside the boxes are all records of financial transactions.
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