One reason is the separation of data storage and application. If you you put both in their own container, you can update them independently. In my experience this is a common process, because usually the application will evolve faster than the underlying database.
It also frees you to run the containers in different places, which might be a constraint in your operations. Or to run multiple containers from the same database image with different applications.
Often it is also a good thing to be able to scale the UI from one instance to multiple instance, all connected to the same database (or cache instance or HTTP backend). This is mentioned briefly in the docker best practices.
I also understand the urge to run multiple processes in one container. That's why so many minimalist init systems/supervisors like s6 came up lately. I prefer this for demos of applications which require a couple things, like an nginx for frontend, a database and maybe a redis instance. But you could also write a basic docker-compose file and run the demo with multiple containers.
