How a node verifies a transaction

A consensus rule is a rule whose violation makes a block invalid. The block subsidy may not exceed the scheduled amount. A transaction may not spend an output that does not exist or has already been spent. A block's proof of work must meet the target set by the difficulty adjustment. These rules are enforced identically by every node, and a node that accepted a block breaking one of them would compute a different chain from everyone else and be ignored. Consensus rules are what make the network a network rather than a collection of opinions.

Policy is everything else. A node's mempool is its own; it decides what it will hold and relay, and different nodes decide differently. The default policy in Bitcoin Core sets a minimum fee rate below which a transaction will not be relayed, limits on the size and standardness of scripts, and rules about how many unconfirmed ancestors a transaction may have. These settings are not part of the protocol and can be changed by anyone running a node. A transaction that one node refuses to relay may be perfectly acceptable to another, and a miner is free to include it in a block regardless.

The practical consequence is that policy shapes what most transactions experience without ever being able to make a valid transaction impossible. A very low fee transaction may sit unrelayed for a long time, but it is not invalid, and if a miner chooses to include it the network will accept the block. This is why fee estimation is a matter of local judgement rather than a protocol constant, and why the mempool page describes a node-local structure rather than a global pool.

The design choice that makes this work is that validation is not delegated. A node does not ask a trusted server whether a block is valid, and it does not accept a block because most other nodes seem to have accepted it. It checks the block itself, using rules it enforces independently, and it will reject a block that the rest of the network has accepted if that block breaks a rule it knows. The cost is that every node does the same work, which is wasteful in the narrow sense. The benefit is that no participant has to trust any other participant's word about the state of the ledger.

This is what people mean when they say that running a node is how you verify your own money. A wallet that queries someone else's server is trusting that server to report the chain honestly. A node that validates for itself is not. The two arrangements look similar from the outside and are quite different underneath, and the difference is entirely a matter of who performs the checks described above.

The block size and weight page explains the limits a block must respect, and the Script page covers the language a node evaluates when it checks a spending condition.