Proof of Reserves
A published check that a custodian holds assets matching what customers are owed, usually combining cryptography with on-chain balances.
The standard construction builds a Merkle tree of customer balances and publishes the root, so each customer can verify that their own balance was included in the total without seeing anyone else's, while the firm proves control of wallets by signing messages or moving small amounts. The mechanism is genuinely useful for the asset side, and genuinely incomplete on the liability side, because a firm can omit liabilities from the tree, and nothing in the scheme reveals debts owed off-chain. It is also a snapshot, so assets borrowed shortly before the measurement and returned afterward will appear as reserves. A meaningful exercise pairs it with an independent audit covering liabilities, and repeats it frequently rather than once.
In practice
Some exchanges publish a Merkle root each period and provide each user a path proving their balance was counted in the total the reserves are compared against.
The common misunderstanding
That proof of reserves proves solvency, when without a verified and complete liability side it shows only assets at one instant, which can be temporarily borrowed.