This is a system that has all the elements of any computer namely CPU, Memory, Input/Output, but it is all on one (small) circuit card or even a single chip.
In earlier days a microcomputer used to refer to a personal computer. For example the BBC Micro in the 1980's. But this term now tends to be used to describe even more compact computers than the PC.
Sometimes 'micro-computers' are also called 'micro-controllers' as many of them are especially designed to control something rather than run general purpose applications. For example you could have a micro-computer (or micro-controller) running your washing machine, or controlling a lift and so on.
The difference between a micro-computer and a microprocessor is that a micro-computer tends to have a complete set of input-output channels ready for use by the equipment to which it is connected, whereas a microprocessor chip will need other electronics to support it.
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