The term Analog audio is typically used in contrast to digital audio. Strictly speaking; audio is used to describe things having to do with sound.
Sound is short-term variations in air pressure above and below average (barometric) air pressure. These pressure variations are translated by a transducer such as a microphone into voltage variations for transmission or reproduction via another transducer (speaker) after amplification. The voltage variations change proportionally to the air pressure variations, so one can say the voltage variations are analogous to the sound- or that the voltage waveform is an "analog" of the acoustic waveform of the pressure variations.
In a similar manner, analog magnetic tape recording utilizes variations in the strength of the magnetic field down the length of the tape to make an analog recording. Vinyl records are engravings of the waveform in the physical medium of the disk. The variations of the groove walls are analogous to the sound pressure variations.