Basics of computer hardware

A computer is a programmable machine (or more precisely, a programmable sequential state machine). There are two basic kinds of computers: analog and digital.
Analog computers are analog devices. That is, they have continuous states rather than discrete numbered states. An analog computer can represent fractional or irrational values exactly, with no round-off. Analog computers are almost never used outside of experimental settings.
A digital computer is a programmable clocked sequential state machine. A digital computer uses discrete states. A binary digital computer uses two discrete states, such as positive/negative, high/low, on/off, used to represent the binary digits zero and one.
The French word ordinateur, meaning that which puts things in order, is a good description of the most common functionality of computers.