Digital means that information is translated to numbers. This results that the message can be divided in well-defined parts that have a clear value (e.g. 0/1, a..z, word etc.)
In analogue communication if you take two values, there is always a possibility to express a new value inbetween them.
Compare digital vs. analogue clock: at the digital clock it shows exactly 12:24. The analogue clock (in theory) when it goes from the 24th minutes to 25th it goes proportionally with the time (see with red, dotted).
Another major difference: a digital message can not be partly processed: or it is fully processed or nothing. An analogue one is more diffuse: if you take out some information, that also might have a particular meaning (but less punctual).