A definition :
“A specialized computer system which is dedicated to a specific task. Embedded systems range in size from a single processing board to systems with operating systems (ex, Linux, Windows® NT Embedded). Examples of embedded systems are medical equipment and manufacturing equipment.”
www.systemsoft.com/l-2/l-3/support-glossary.htm
With the family that is embedded systems including toasters, games consoles and intensive care monitoring equipment, an elegant definition is hard to come by.
Suffice to say, if your product uses a microprocessor and is designed for a specific application, it probably falls into this category.
Some of the common characteristics of embedded systems are :