A digital controller receives input signals measuring properties like impedance, compares the actual values to targets, and sends control signals to adjust components accordingly. It works by measuring the actual state of a device, comparing it to the target state, and taking action to stop or allow heating as needed. Digital controllers offer advantages like flexibility, inexpensive implementation using microcontrollers, and resistance to environmental impacts compared to analog controllers. They are commonly used in industrial heating systems to stably control temperature within safety limits.