An embedded system is the combination of the software and hardware that controls a larger system to achieve specific functions. It can be found everywhere in a computing system but not a general purpose computer itself is not considered as an embedded system since it is multi-functional. The embedded system usually takes an analog or digital input and processes it based on the software and the hardware embedded to return certain output. Some of them has user interface, but it still deals with fixed set of instructions.
To summarize the main characteristic of an embedded system, it is designed to have specific function and the commands are executed repeatedly. Efficiency is the primary concern of an embedded system, since embedded systems are typically designed to meet real time constraints. Embedded systems often interact (sense, manipulate & communicate) with external world through sensors and actuators and hence are typically reactive systems. Some of the embedded systems have a user interface but it is not ubiquitous.
Embedded systems are usually based on micro-controllers, microprocessors, System on Chip (SoC), and Field Programmable Gate Array (FPGA). A micro-controller is a functional computer system on one chip containing an integrated processor, memory, several peripheral devices, and serial communication devices. A modern SoC can include one or several CPU subsystems to execute software and sophisticated interconnects. FPGA is a fully programmable alternative to a customized chip.