Recording audio in a format of continuous vibrations that are analogous to the original sound waves. Before audio recording became digital, sounds were "carved" into vinyl records or written to tape as magnetic waveforms. See audio cable
Sound is literally carved into a phonograph record because the groove undulations are analogous to the sound waves they represent.
Analog vs. Digital
The 78 RPM record (left) contains about four minutes of analog audio per side. The digital disc (right) holds about an hour's worth of CD music (CD-DA format) or 10 hours of MP3 songs.