To talk about the more specialized use-cases: there are some truly novel things that can only be done with the blockchain. To give you a direct example -- 'provably fair' gambling enables someone to place bets and know for certain that the result will be fair. This is accomplished by having outcomes enforced for a network of computers instead of trusting some shady website to stay fair. It's basically fully transparent. I know there will be people saying that this grasping at straws but the list of use-cases is quite long. I don't have time to research and list all the interesting ones here. But if anyone is interested in the subject I promise you that learning more about it won't be a disappointment.
It's just not easy to explain in short-form posts.