What "local processing" means technically
Local processing means the conversion runs on your device's own CPU, using your browser's WebAssembly runtime, rather than being sent to a remote server to run on someone else's hardware. You can confirm this yourself: open DevTools' Network tab during a conversion and you'll see no outbound request carrying your file.
This also means PrivaPDF keeps working on air-gapped or network-restricted machines once the page has loaded — there's no ongoing dependency on a live connection to a backend, because there is no backend involved in the actual conversion.