Microcomputer is a small computer (compared to big supercomputers) that has a microprocessor (again, the term 'micro-' in this word is now eliminated and it is just called processor), central processing unit (CPU). Your PC is an example of a microcomputer. A Microcomputer is a complete system consisting of (usually) a Microprocessor, but could be a complete system consisting of a Microcontrolle
Microcontrollers are computer chips that (if you look at its name it becomes obvious) control something. Microcontrollers usually have a processing unit (which usually runs on a low clock speed), internal memory and input/output elements. Pretty much every electronic device has a microcontroller - starting from a game console or electronic clock and ending with personal computers. A Microcontroller typically has (small) internal memory and internal peripherals. They are generally slower to mid performance. Usually a Microcontroller based system is called an embedded system
Microprocessor is also called the Central Processing Unit (CPU). A microprocessor is currently working in your PC and it's either from AMD or Intel (or any other processor manufacturer). Basically, a microprocessor is one of the essential elements of a computer, as it handles all the operations a computer performs. A Microprocessor typically has (large) external memory and external peripherals. They are generally higher performance.