Accessing data with permissions towards access only going to specific, pre-determined parties. Brings blockchain in line with the current data control paradigm by doing so.
With a conventional database, the owner can set any value to anything they like.
With a private blockchain (and smart contracts), the owner can't forge values.
For example lets say you want to fake a transfer from client A to client B. In a traditional database, the owner can do that. With a blockchain, the owner can't.
And every actor will know there's a double spend attack and stop accepting the chain. Unlike a public blockchain, there should never be a fork in a private blockchain. If there is a fork, you know the owner is mounting a double spend attack.