How does Bitcoin verify payments without a central bank?

Detailed explanation

A bank keeps accounts in its own database. It verifies identities, authorizes entries and decides which balance is authoritative. Bitcoin instead uses a publicly verifiable transaction register. It contains no traditional named bank accounts, but transaction outputs that can be spent under defined conditions.

Someone wanting to spend bitcoin creates a transaction and uses a digital signature to demonstrate control of the required keys. Nodes check, among other things, that the signature is valid, the values used exist and they have not already been spent. Miners can include valid transactions in blocks and thereby order them. A miner cannot, however, make an invalid spend valid if nodes reject it under their rules.

Bitcoin thus replaces certain tasks of central account management with cryptography, a shared register, economic incentives and distributed verification. It does not remove every form of trust. Someone using an exchange, third-party wallet software or a custodian may still depend on that party's security and honesty. Bitcoin's underlying history can nevertheless be checked without a bank as sole bookkeeper.