If you turn on project watching, you'll be getting notifications about all the activities on a project. Turning on watching a project doesn't make you a project member. It just allows you to get notified about all the stuff that goes on. Read here how to join a project.
This could be useful if you want to track certain projects and be notified in real time what's going on.
Switch between watching and not watching a project by clicking on the eye icon.
Go to More actions menu and select Edit project option.
Change the name of the project, person responsible for the project or the company. You can also make a project private or public.
Is there a way to delete a project you might ask? There isn't.
You can't delete a project, you can archive it.
And if you ever change your mind you can restore it back.