In this quote, Satoshi is addressing a potential concern about the scalability and complexity of the Bitcoin network. Specifically, he's talking about the issue of "fan-out," which refers to a situation where a single transaction depends on multiple previous transactions, and those transactions in turn depend on many more previous transactions, creating a complex web of dependencies.
Satoshi is saying that this kind of fan-out is not a problem for the Bitcoin network because the network doesn't need to store or transmit a complete, standalone copy of a transaction's entire history in order to verify and process it.
In other words, when a new transaction is broadcast to the network, it doesn't need to include a complete record of all the previous transactions that it depends on. Instead, the network can simply verify that the transaction is valid by checking that the inputs (i.e., the coins being spent) are valid and that the outputs (i.e., the coins being received) are correctly calculated.
The reason this is possible is that the Bitcoin network uses a data structure called a "blockchain," which is a decentralized, distributed ledger that stores a record of all transactions that have taken place on the network. Each block in the blockchain contains a set of transactions, and each transaction includes a reference to the previous transactions that it depends on.
When a new transaction is added to the blockchain, the network can verify its validity by tracing back the chain of dependencies to the original coinbase transaction (i.e., the transaction that created the coins in the first place). However, this process doesn't require storing or transmitting a complete copy of the entire transaction history. Instead, the network can simply follow the chain of references to verify that the transaction is valid.
So, Satoshi is pointing out that the Bitcoin network is designed to handle complex webs of transaction dependencies without requiring a complete, standalone copy of each transaction's history. This makes the network more scalable and efficient, and allows it to handle a large volume of transactions without becoming bogged down in complexity.