A coin is a chain of signatures
Section 2 gives a surprising definition: an electronic coin is a chain of digital signatures. Each owner passes the coin on by signing a hash of the previous transaction together with the public key of the next owner. Anyone can follow the chain back and check every signature.
Signatures prove that the owner agreed to the payment. They cannot prove that the owner did not also sign a second payment of the same coin to someone else. For that, everyone needs to agree on which payment came first.
A timestamp server
Section 3 proposes a timestamp server: take a block of items, hash it, and publish the hash widely. Each new timestamp includes the previous one in its hash, so the timestamps form a chain, and each one reinforces the ones before it.
The word blockchain never appears in the paper. It speaks of blocks and of a chain, and the name came later from the community.
▶ SEE IT IN THE MACHINEOn the BLOCKCHAIN rail, each block is locked to the one before it by its tenon, the hash of the previous block.