As stated at http://www.esacademy.com/automation/faq/primer/2.htm:
An embedded controller is basically a controller (typically a microcontroller, microprocessor, or computer) that is embedded into some [system or] device for some purpose other than to provide general purpose computing.
This device would be called an Embedded Control System. Some examples might be a home appliance or toy with a microcontroller inside of it or a factory automation system that contains a dedicated computer control box.
What is a Microcontroller?
According to wikipedia:
A microcontroller (also MCU or µC) is a computer-on-a-chip. It is a type of microprocessor emphasizing self-sufficiency and cost-effectiveness, in contrast to a general-purpose microprocessor (the kind used in a PC). In addition to all arithmetic and logic elements of a general purpose microprocessor, the microcontroller usually also integrates additional elements such as read-only and read-write memory, and input/output interfaces.
Microcontrollers are IC chips and need to be put onto a custom-designed PC board. This takes time and money, which may not suit all applications. Contrast this with an industrial automation PLC, which is a computer-in-a-box that contains simple screw terminals to connect power, communication, and I/O.
Programming microcontrollers requires a certain amount of skill and training.
The programming and debugging software can be quite costly.
Microcontroller Architecture Example
An example of a simple microcontroller is shown here embedded in a system: