A main component of natural interactions is Direct Manipulation. Traditional interaction methods (keyboard) are very efficient but often very unnatural because what do you do and what happens on screen aren't necessarily very logically connected. This was a classic problem with command line interfaces (or worse, punch cards). The Graphical User Interface was largely a hit because of the Direct Manipulation it affords. As a bit of trivia, Video Games, especially Pong, quickly showed the ease of control direct manipulation can give people.
With touch interfaces you directly touch what you want to interact with, making buttons extremely natural. Panning and zooming might not occur exactly as they do with real world objects, but they operate exactly and move fluidly due to your manipulation. Move your finger 10 cm in a pan gesture and the screen scrolls 10 cm with your finger.
It's been shown repeatedly that users love Direct Manipulation. It creates an effective, engaging interface and allows the user to feel in control. Even if the exact action (like panning) isn't 100% intuitive, it is extremely easy to learn. The causality is very clear, leading to very few "wait, what did I press?" moments.
