docker-compose is a way of managing your containers, instead of using “docker run”, you can use compose to make a recipe of your container, so you dont have to remember your docker run command.
The supervisor part is true though, what docker does, is that it starts 1 application when it starts, it could be apache, but it could also be something like supervisor, and then supervisor spawns cron and apache.
There is some examples of this here or i made an complete example here