This is an example of how a transactions can be represented as a "chain of digital signatures". It is not exactly how bitcoin operates because it does not take into account Section 9. "Combining and Splitting Value", nor does it take into account Section 10. "Privacy".
In the diagram you've linked to, the left hand box demonstrates the original owner (Owner 0) of some predefined value transferring ownership of that value to someone new (Owner 1).
The "hash" in that box would be the hash of the "coinbase" transaction where that value came into existence (indicated by the arrow coming in from the left of the image). This previous "coinbase" transaction would have Owner 0's public key. Owner 0 proves his right to transfer the value by providing a digital signature using the private kay that matches the public key stored in the "coinbase" transaction. Owner 0 turns over control of the value to Owner 1 by providing Owner 1's public key. As such the only person who can now re-assign the value is the person who has the private key that matches the public key in this transaction and can therefore provide the appropriate signature.
So in this diagram a "transaction" consists of 3 parts:
- A hash indicating a previous transaction that transferred the right to reassign the value to the current owner.
- A signature provided by the current owner indicating that they are transferring the right to reassign the value to someone else
- A public key, setting up the signature requirement for the new owner to reassign the value
As you can see, each of the next two boxes simply repeat this process.
The dotted lines are showing that the signature is provided by the current owner's private key, and that the entire network can verify that signature since the public key is provided in the previous transaction.
