Embedded system is basically a combination of miniature computer and a real-time operating system (or often just a controlling program). These systems are used in places that require computer-grade logic systems, but are too risky or demanding to implement with "normal" computers and operating systems.
An example of this would include a car. Modern cars have several embedded systems that control all sorts of things in the car, but the "user" (the driver and the passengers) doesn't need to be aware of these computers. Or, one might find an embedded computer from a cell phone - that has an user interface that is clearly computer-controlled, but not many people think it is a computer.
Embedded systems are usually built for specific purposes. Often, an embedded machine has just a single component board with OS and programs on ROM chip, and only what's required for the computer to interface with the world.
See: Ubiquitous computing, real-time operating systems