What's the benefits to using analog-to-digital conversion like PCM?
As with most things in engineering, it depends on the trade offs.  If you want to add complexity in order to gain noise immunity, then yes the book is correct.
However, maybe you have a circuit where the analog source is only 0.1&quot; away from the A2D, would I put a PCM circuit for that? No!
Maybe you have an analog sensor that requires an op-amp for some reason, now you have a nice low impedance driver, which can withstand noise better, so again, PCM isn't needed.
There are more applications for PCM than what I've described check Wikipedia:
Wikipedia on Pulse-code_modulation
To specifically address the questions:

how is a digital signal superior to an analog signal?

This typically has to do with noise immunity. An analog signal with 100mV of noise on it is most likely not very usable.  However a digital signal with 100mV of noise on it will work just fine.  Look at the Vih and Vil of almost any digital chip as a starting point.

What's the benefits of changing an analog signal to digital data?

This usually has to do with a storage requirement like in CDs(check the Wikipedia link), or transmitting over long distances or on a medium that only supports digital signals.  In the later two cases, it really boils back down to noise immunity.