A CBDC is a digital form of currency. It is issued and regulated by a central bank. It is a numerical representation of a fiat currency and collateralized by currency reserves (precious metals such as gold or local/foreign currencies) to guarantee the stability of the value. CBDC's can be used as a method of payment, value reserve or unit of account.
There's been multiple test cases of this particular concept in practice on Tezos, one resulting in a Euro stable coin for Tezos.
Examples on Tezos:
Société Générale is one of the leading European financial services groups. In September 2020, Société Générale - Forge selected the Tezos blockchain for experimentation with CBDC research and development. This is ex post facto of Banque de France selecting Société Générale - Forge as part of its group to experiment with CBDC technology around interbank settlements in July 2020.
As of today - French startup Lugh has launched a new Euro stablecoin (Lugh) on the Tezos blockchain, with associated bank deposits held by Société Générale and audits from PwC and Maghreb.
In November 2020, it was announced that BNP Paibas alongside CA CIB, Caisse des Dépôts, Tokeny and Blockchain Xdev (The Blockchain Group) were combining expertise to launch a project exploring the potential use and implications of Digital Interbank Currency (DIBC). Tezos and Ethereum were chosen as initial technologies for exploration.