There are two main types of computers: analog computers and digital computers. Analog computers represent and manipulate data using continuously variable aspects like voltage, while digital computers use discrete binary digits. An example of an analog computer is an educational model from 1960 that used electrical, mechanical, and hydraulic components to model problems. In contrast, digital computers like mainframes represent data using binary and can only be in two states, requiring many transistors for precise values. The key difference is that analog computers perform calculations in parallel using continuous variables like voltage, while digital computers work sequentially in discrete steps using binary digits.