Take Preet Bharara as an example. Trumps DOJ, when they first came in, asked some federal attorneys for their resignations. Preet had been one of them, and he failed to give in his resignation. He was then terminated.
Thanks a lot! So that's something specific to cabinet members, if you're a random worker you don't have to wait for your boss to accept your resignation?
I wouldn't say its specific to cabinet members, nor the President.
Your boss could ask for your resignation if you've been there for 10 years and you're eligible for a pension, or healthcare in retirement. And instead of fighting it and being fired, you could accept whatever your job is giving you to walk away -- instead of having to be fired and losing all of this (if you had done something wrong on the job)
But I know that it is most typically cited as being done in politics. As you want a team of people below you who support your cause.