Analogue distinctions have discrete variations, as in an analogue watch. This is as opposed to Digital. You can notice time pass with analogue (as in the hands of a watch ticking), in digital you just see result, but not the passage it went through to get there.
Here is a technical definition:
An analog or analogue signal is any variable signal continuous in both time and amplitude. It differs from a digital signal in that small fluctuations in the signal are meaningful. Analogue is usually thought of in an electrical context, however mechanical, pneumatic, hydraulic, and other systems may also convey analogue signals.
An analog signal uses some property of the medium to convey the signal’s information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. Electrically, the property most commonly used is voltage followed closely by frequency, current, and charge.
Any information may be conveyed by an analogue signal, often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure, and is achieved using a transducer.
For example, in an analogue sound recording, the variation in pressure of a sound striking a microphone creates a corresponding variation in the voltage amplitude of a current passing through it. An increase in the volume of the sound causes the fluctuation of the current’s voltage amplitude to increase while keeping the same rhythm.
Since most natural data is analogue before the digital conversion required to get a digital signal, resolution of analogue recording and transmitting technology has been higher until recent times. For practical reasons such as memory conservation and the cost of phasing out older digital recordings, the resolution of some digital signals may remain lower than most analogue signals. For this reason, some audiophiles prefer analogue technology. However, in many cases, the difference is too minimal to be noticed.