A system which contains a processor, but is not itself a computer.

The definition starts getting a bit fuzzy at the extremes; eg, when people start talking about "embedded PCs"

Some people use the term "deeply embedded" when there is no separate processor chip, but it's implemented as a "core" inside some other VLSI device.

eg, some telecoms chips actually have, say, an ARM processor core within them, although they might just be called an "E1/T1 Framer" or something, and you wouldn't have to write any software or anything to use one in your design.