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We are all familiar with what a computer is in a specific, contemporary sense. Personal computers (PCs) are found in most aspects of daily life, and for some it is hard to even imagine a world without them. But the term means more than simply the Macs and PCs we are familiar with. A computer is, at its most basic, a machine which can take instructions, and perform computations based on those instructions.
It is the ability to take instructions — often known as programs — and execute them, that distinguishes a computer from a mechanical calculator. While both are able to make computations, a calculator responds simply to immediate input. In fact, most modern calculators are actually computers, with a number of pre-installed programs to help aid in complex tasks.
Computers range from the very small to the very large. Some are capable of doing millions of calculations in a single second, while others may take long periods of time to do even the most simple calculations. But theoretically, anything one computer is capable of doing, another will also be able to do. Given the right instructions, and sufficient memory, a computer found in a wristwatch should be able to accomplish anything a supercomputer can — although it might take thousands of years for the wristwatch to complete the operation.
At one time, computers were extremely large, and required enormous amounts of power. This made them useful only for a small amount of tasks — computing trajectories for astronomical or military applications, for example, or code breaking. Over time, with technological advances, they were scaled down and their energy requirements lowered immensely. This allowed the power to be harnessed for a staggering array of uses.
As prevalent as PCs are, they do not nearly begin to scratch the surface of computer use in our world. Interactive devices of all sorts contain their own computers. Cellular telephones, GPS units, portable organizers, ATM machines, gas pumps, and millions of other devices all make use of them to streamline their operations, and to offer features which would be impossible without one.
A computer like this is often referred to as an embedded computer. The embedded type is differentiated from a PC because it is essentially static in its function. While a PC, some cellular telephones, and some personal organizers are able to have new software installed, and make use of a wide range of features, an embedded computer usually has only a few purposes, which are relatively fixed once the device is manufactured.
Embedded systems vary in the amount of change that can happen to them after production. An MP3 player, for example, is an embedded computer, but can have quite a bit of interaction and changes made to it. It may allow the user to alter the colors used, change the clock, update firmware, and change the songs or playlists in memory. One within a traffic light, to take another example, is probably quite fixed. It is set to respond to a few certain programs — time of day, a trigger when a car approaches, and perhaps input from a central database in the case of more advanced systems. These programs are not built for interactivity, and will likely never be changed over the system’s life.
The computer is one of the most powerful innovations in human history. With their use, people are suddenly able to perform a staggering amount of computations at dazzling speeds. Information can be crunched, organized, and displayed in the blink of an eye. As technology continues to advance, the computer will no doubt become even more pervasive — and in many cases, likely even less recognizable.

http://www.wisegeek.com/what-is-a-computer.htm 

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