A microcontroller is a small, single-chip computer optimized for low cost, realtime performance and low power consumption rather than peak computing power. They typically have no operating system (or a minimal OS like FreeRTOS) and custom hardware peripherals such as hardware interrupts and timers, I2C, SPI or UART serial devices, and built in ADCs/DACs. This allows them to easily interface with other electronic devices like motors, rotary encoders, or other ICs.
Microcontrollers are typically embedded into larger electronic devices to provide the necessary control logic. Additionally, they are often available on "dev boards" that provide power conditioning, solder-free access to the I/O pins and often a method of programming the microcontroller directly via USB, for hobbyist or developer use. The most famous of these is the Arduino.
Your typical Robowaifu project will nearly always include at least one microcontroller. A complex robot can have dozens.