In general, microcontroller usually contains a host of onboard features that allow them to operate without the need of external ICs. Microcontrollers have their memory onboard so there is no need for additional external memory. Common microcontrollers include the PIC (from Microchip) or an AVR (from Atmel).
Microprocessors are usually more powerful (think Pentium Processor) and unline a microcontroller require a host of external parts including external memory.
