Square waves or 1's and 0's?

first you need to understand a meaning of analogue signal, than modulation, than sampling, than binary algebra.

otherwise any technical content will seem to be confusing.

digital signal not only has ones and zeroes, but rather characterised by sampling frequency and sampled amplitude as mentioned before voltage level.
an arbitrary point of signal could be captured knowing the particular voltage and the value of the signal 0(low) or 1(high). The low could be let's say 0V and high could be +50mV etc...

0-s and 1-s are only rererence values of digital signal, but not the actual physical ones for those who thinks that 0s and 1s are 'traveling' accross the digital cable.
electrones are the only ones capable of doin' that

that was a true statement Lynne simply because digital cable carries simple shape signal compared to an analogue music.

There's no waveforms in the Universe that are not continues. That also applies to square pulse.