Some examples IMHO are logs of participation (e.g. voting), agreements (e.g. contracts), exchange (e.g. payments), and auditing (e.g. compliance).
A blockchain can be public or protected i.e. private just to the participants. A blockchain can store plain text information or access-controlled information i.e. encrypted information or links to sign in systems.
All of these capabilities provide massive trust advantages over a traditional database as managed by a central administrative entity, which requires the participants must trust the central administrative entity to be truthful, unbiased, secure, and with sufficient high availability and disaster recoverability.