They are low cost, low power solutions aimed at relatively simple control tasks where a microprocessor and its support ics would be too expensive and/ or massive overkill. They sit between microprocessors and system on chip devices.
Microcontrollers have a lot in common with microprocessors but they are not high speed number crunchers. They typically use a simple RISC architcture. The small amount of internal memory provided is sufficient for many of applications. You'll get a few registers some ROM and RAM an ALU and a fair bit of IO. Microcontrollers are intended for real time control applications.
Sometimes they are used to relive a central micoprocessor or FPGA system from mundane tasks. eg Reading sensors, analog signals, motor control, reading knobs and switches, operating status LEDs etc. etc.
You can program them through their SPI or I2C serial interface or load from an external ROM. You can add external RAM to some types. Some tyes are OTP. You get the manufacturer to do it for you for bulk orders. More modern mc's have on board encryption to protect your proprietry code. Ethernet and USB interfaces are avaialble on some of the more sophisticated mc's. They can be very compact, available in 8 pin packages. Ideal for your toaster! The have more in the way of control IO such as PWM outputs, on board ADC and DAC voltage ref etc. This makes for a compact autonomous system. They are often be used in stand alone circuit without external ROM or RAM.