You should know your work inside and out, of course. You also need to know the work of everyone who is working for you. You should be able to do their job just as well, if not better than any of them do it.
I know that in business, the thing is delegating: Passing on menial tasks to others to free your time, energy and brain to do more important, top-level work. And that’s a great idea. That doesn’t mean, however, that you shouldn’t know how to do those jobs. For one, you may need to train someone on how you want the job done. Another reason is to make sure that the person is doing the job properly: How can you check their work if you don’t know the work?
A third reason is a principle I read from military leaders: Soldiers won’t respect a general who can’t do the soldier’s job at least as well as the soldier, or a general who tells the soldiers to do a job that the general himself won’t do. You must be able to do everything anyone in the group is doing, and they need to know it. And you’d better be ready to prove it.