How does my computer work?

Well, this question could be answered on many levels. Your computer is a bunch of switches that are organized in such a way that you get meaningful signals out.

Computer programs organize how these switches work together to get the meaningful information. They make use of the existing arrangement of switches to do this. A compiler takes the computer code that you write and puts it in a usable form that can be eventually acted on by the switches. This "usable form" consists of specific voltages. You can either have no voltage (grounded) or have a finite voltage (above some pre-defined level). These are called 1s and 0s. These voltages are what gives you answers to your calculations and makes things show up on your screen. They are the lifeblood of computing.

Now, you may be thinking, what are these switches and how do they work. They can't be the same as a light switch. The type switches used in computers are called transistors. Typically, the ones that are used are MOSFET transistors. I have talked about current and voltage before. Resistance relates these two quantities by (note that V signifies voltage, I signifies current, and R signifies resistance):

V=IR.

By changing the voltage at a gate, the resistance between two other contacts is changed, either allowing or not allowing charge to move between the two contacts. Watch this video if you are interested in a more detailed explanation (or ask in the comments section).