To provide direct and transparent connectivity to the banking system. People can then use it to receive their salary, pay their bills and make transactions.  At the moment we have Bitcoin and other systems which are standalone and are not seamlessly integrated with the general banking system. They are completely separate.

The system would ideally incorporate all currencies recorded in the block information.  The account holder would have just one account number for all transactions, in other words their bank account. But instead of with a bank, its in the cloud, in the blockchain. It runs itself, no need for a bank.

People could have more than one account number if they wanted, for different purposes, businesses etc do this. But basically its differentiating between transaction id's which is what the Bitcoin system is, and proper account numbers which contain transactions.

Setting up such a system I guess could be done solely for Bitcoin initially, then adding the other digital currencies and then adding full fiat currency interfaces.

Another advantage is the level of abstraction. No need to handle the current long Bitcoin addresses, which are not human friendly. Instead you would have a single permanent account number, your Bitcoin bank account number. 

There would also be full IBAN/SWIFT integration as well later on so that it would be fully integrated into the existing traditional banking system.