An analog electronic signal is created by the continuous modulation of some property of the current or wave. For example, in an analog sound recording, the frequency of a pure tone striking a microphone creates a corresponding pulse in the amperage passing through it. An increase in the volume of the sound causes the fluctuation of current to increase while keeping the same rhythm.
The primary disadvantage of analog signalling is that any electrical system has noise in it--that is, random variations. As a signal is copied and re-copied, or transmitted over long distances, these random variations become dominant.
See digital for a discussion of digital vs. analog.