How and why is silicon used in mobile phones and other devices?

The basic building block is a transistor which has layers with different impurities added. These devices use thousands of transistors in a building block. Read about it here.

http://en.wikipedia.org/wiki/Transistor

There is more information there than you need to know.

This reference gives all you need to know about the theory of transistors. The thing you have to understand is that the impurities (deliberately put in) carry a charge. Without these impurities, silicon and germanium are basically insulators. A very tiny current can control a very large one.

http://web.mit.edu/newsoffice/2013/researchers-dem...

Your next step in understanding this process (and the answer to your question) is to look up an integrated circuit. Here many transistors are put together to perform a sometimes complex operation. Recognizing a dial tone and answering it when a button is pushed, is a nightmare in design. Then to translate what you say (we speak in what is called analog which is basically pressure related) into the way transistors think (commonly called digital) is a nightmare in complexity and requires many many transistors to do, hence more silicon and it's amazing ability to control current flow.

All of this requires that the magic be performed in tiny places. Your last step is integrated circuits. Here's what they look like. Tiny you want, tiny you get.

http://www.bing.com/images/search?q=integrated+cir...