One possible application for a distributed ledger could be an application in which multiple entities participate and update their own records. The entities could be the government or other institutions such as banks or financial services firms. They all have the same ledger but they could update it independently.
Another example would be to track the logistics of shipping. This would allow us to trace the amount of imports into the country as well as what is actually being sold. Blockchain would allow for transparency, which is the big advantage of blockchain over other technologies.