Broadly speaking blockchain only solves a singular problem: Trust. If there is some work that needs to be done between parties and you don't trust the parties involved then you can use blockchain to do the work in a trust-less setting. This is why money has been the first and most prominent use case; people are less trusting with their own money.

For a specific non-money potential use case of blockchain I would say identity services. For example, currently the internet runs based on implicitly trusting a set of root CAs (hundreds just counting the big ones!). The CAs certify that a site is what it claims to be. But if the CA becomes malicious (either through intent or hack) there are limited mechanisms for combatting this.

If you decentralize the certification process you can have a trust-less system. This also works beyond CAs - any sort of identity management falls under the same principle: Credit scores, citizenship, etc