On-device transcription starts with a model file on disk. At runtime the app loads it onto the CPU, GPU, or a dedicated neural accelerator and feeds it audio buffers. There is no magic privacy from the file sitting there — the gain is that recognition does not need to copy the waveform to someone else's GPU. First launch is often slow because of the download and compile step. Later launches reuse the cached model. Hardware bounds are real: machines with less memory struggle with large checkpoints, especially if you also run a local language model for cleanup.
On-device is not a synonym for 'never uses a network.' The app may check for updates, sync settings you opt into, or offer a cloud engine as a second mode. The scoped claim is about where transcription happens when the local engine is selected. It also is not a synonym for 'more accurate': a huge cloud model can beat a tiny local one on some audio, while a strong local model can beat a cheap cloud endpoint. Compare engines, not slogans.