Crypto-currencies are digital-only currencies the methodology used for encrypting and registering it is used to monitor and regulate the generation of the monetary unit, and this is not under the purview of any banking entity. The methodology is called blockchain.
Blockchains use data structures using an anonymous network to help carry the transactions by securely altering the structure, and they do this without the support of any third party, unlike the banking operations which are connected to a centralized network. The algorithm which helps the blockchain eliminates the need for people to verify the transactions because the blockchain database fetches the input values and molds them into a block.
Each such block is chained to another block using a cryptographic signature. This can be accessed by anyone who has the permission to do so and hence this eliminates the third party which in the conventional sense is the central banking network. The advantage around this system is the security it offers along with the anonymity and freedom from banking fees and transaction charges.