How can a touchscreen tablet be both an input and an out put device?

Touchscreens have a thin layer of sensors that act just like your keyboard. Each tiny square has a point coordinate or a specific address, just like the keys on the keyboard, so when you touch the left bottom corner, the sensors go off and send an "on" signal to your computer telling it that there is input in that specific area, your computer processes the information and outputs a dot, or moves the mouse pointer to the left bottom corner.

My description is of course very high level, I hope it gives some clarity to your question though.