Full Reserve Banking
A Full Reserve Banking or 100% reserve banking system is one in which banks must hold reserves for 100% of on-demand liabilities. This means that should on-demand creditors all simultaneously ask for repayment, the bank will be able to honour all its obligations. This contrasts with a system of Fractional Reserve Banking.
Term-deposits and other time liabilities are not limited by a full reserve banking policy. However the bank should plan to have enough reserves when their term expires and these debts become enforceable. "The date on which the bank's obligations fall due must not precede the date on which its corresponding claims can be realized. Only thus can the danger of insolvency be avoided." (Ludwig von Mises. The Theory of Money and Credit. 1912).
Proof of Reserves
In the Bitcoin world, inasmuch as exchanges have acted like banks by holding user Bitcoin balances, we have seen instances of Fractional Reserve Banking practices and also bank-runs leading to insolvency. Most notably in the case of Mt. Gox. Since then Bitcoin exchanges and other companies acting as Bitcoin custodians have started to offer cryptographic Proof of Reserves, Multisignature vaults, third party audits and other ways for users to verify that the company's Bitcoin liabilities in the event of insolvency do not exceed reserves.