Please see this answer in the english stackexchange site on the origins of "analog", where it is discussed how the term specific to electronics came to use in the 40's with the emergence of digital computing (and in contrast analog computers before that).
However I don't find the definition "anything we can count" as simple or clear, as I would not necessarily associate anything meeting that description as being "digital" (I can count my siblings and yes they have fingers but I still don't call them digital).
With reference to signal processing (the topic of this forum), I like the definition "digital is any signal that is discrete in time and discrete in magnitude", which Marcus Mueller had pointed out here is the definition provided by Oppenheim and Shaeffer with no other caveats. I find it to be both concise and complete. Digital electronics work with signals and data that meet this definition. If we want to concern ourselves only with what can be plausibly implemented in computers and hardware, we can then add the caveat that it also must be a finite number of elements as @AlexTP proposed in the comments to this related post. (However typically workingwe often work with abstractions that go to infinity in time or in magnitude should, so this shouldn't exclude a waveform from being "digital" IMO. (I can certainly picture cases of waveforms that extend for infinite time, but must admit that I can't yet conceive of a practical application, meaning mathematical convenience, of extending a digital waveform to infinite magnitude).