Whenever you create a child of an existing item, the context defaults to that of the parent. If you have set a context for a project, actions you create or move into that project will get that context, unless you specify otherwise. If you are creating a project where many actions have the same context, this can save you some work.
When you complete all the actions in a project or action group (the term for nested actions), the project or action group itself becomes available, looking much like an ordinary action, but for the bold styling. This gives you notice that you've completed all of the actions you set out, and it is time to either add some more, or mark the project or group as complete. Setting the context of a project or action group allows you to choose in which context this item will appear. If you want to complete it, you just check off the project, and it is as if you had edited the project and set its status to Completed.
A search for "Show projects and action groups in context mode" will find you previous threads on this occasionally contentious topic. Some people prefer not to see the project and action groups in context mode. If you are one of them, see my post
here for details on how to be rid of them.