Hardware debugging involves monitoring signals, checking connections between components, and testing circuit continuity on a target board. This process identifies issues like dry soldering, missing connections, or unnoticed PCB errors that could prevent firmware from functioning properly. Key tools for hardware debugging include a magnifying glass for visual inspection of soldering and tracks, a multimeter for checking continuity and signal values, an oscilloscope for analyzing waveforms and noise, a logic analyzer for capturing digital data, and a function generator for simulating input signals.