Analogue electronics handles analogue signals. Analogue signals are signals having continuously varying amplitudes with respect to the time. For example the loudspeaker of a TV set or of a radio receives a voltage that usually is continually changing, which in turn causes a current to flow that changes in the same way and that activates the speaker cone to move, causing sound. This is an analogue device.
Digital electronics handles digital signals. Digital signals are discrete signals. They have constant amplitude for a specific time period. Walking could be regarded as similar to a digital device. The number of steps per minute can vary, but each step is usually nearly the same. A digital signal can be regarded as a number "packages" that are almost the same, but the number of these packages that are delivered per minute varies.
In another context, there are analogue watches and digital watches. The analogue watches have a minute hand and an hour hand, they keep moving all the time, while a digital watch has numbers showing, they change only once in a while.