This paragraph is talking about a way to create a timestamp server that works on a peer-to-peer network.
Instead of using newspaper or Usenet posts like the previous method, this new method involves a “proof-of-work” system similar to Hashcash.
This means that the system requires work to be done by the computer to prove that a block of data exists at a certain time.
This is done by scanning for a value that when hashed, starts with a number of zero bits.
The more zero bits required, the more work is needed.
Once the work is done, the block cannot be changed without redoing the work, which makes the system secure.
The system also uses a “one-CPU-one-vote” approach to decision-making, where the longest chain with the greatest proof-of-work effort invested in it represents the majority decision.
The difficulty of the proof-of-work is adjusted over time to account for changes in hardware speed and interest in running nodes.