Example: you might take a fingerprint of a recorded interview and save that to a block chain. When you distribute the interview the receivers can verify it hasn't been tampered with based on the fingerprint and when it was added to the chain.
This way you don't need to trust the source of the video or the person giving you a fingerprint, as that's stored immutably.
The limiting feature of blockchains is that they cannot integrate with real world (i.e. non-blockchain) data without trusting the data provider. And at that point, the key feature of blockchains (no need to trust anyone) is completely lost.
In case of a video, blockchain could be used to tamper-proof security footage. You can always manipulate the incoming data (cover the cameras etc), but once data has been recorded (whatever it may be), there's no going back and overwriting it.
I'm surprised how oblivious the HN crowd is to how huge this is for the enterprise and government sector where data like land registry or citizenship records (see Obama's birth certificate, GWB's military record) have to be kept provably untampered for up to a century.