What does it mean if your toliet is clogged and water is coming up through the tub and shower drain?

It means that your main drain line is clogged downstream from where your drain from your tub ties into your toilet drain and the problem can be a hundred of different reasons. The first thing I would check is your clean out (if you have/find one) outside of your home usually within 2 to 5 feet from your outside wall. If you do find the clean out then take off the clean cover and see if your clean out pipe is full of sewage ( becareful of taking off clean out cover because it might have a lot of pressure behind it if clogged) If you can not find a clean out then if possible wait till the tub drains and then use a shop vac to vacuum out the toilet and then pull the toilet and snake down the toilet drain or if you find a clean out then snake down the clean out. When you run a snake down the clean out or toilet drain if possible run water down it too while you snake the drain line. Most drain lines do not plug up if they are plumbed in right which means have the right grade and have the right fittings so back to your question this could be possible that you have a problem in your drain line and I would (after you clear the line) check it with a camera other wise you might have to snake out your drain line often.