I'm 2 months into my PhD. When can I ask my supervisor about the rejected candidates? I was recently accepted for a PhD position after going through the application process of submitting the usual documents (CV, motivation letter,...) as well as an interview. 

I have heard, from my now colleagues, that during the application process, my supervisor had mentioned that I had come across as very motivated.

I am curious however, if there is ever a good time (say after one has established a rapport with one's supervisor) to ask about the other candidates who fell short? Or is it something quite taboo?
You can ask, but it's really none of your business.  Admissions committee deliberations are generally treated as confidential.  Asking about the other candidates and why they were rejected will almost certainly be seen as intrusive.  It's the kind of thing that's likely to cause them to wonder how they made the mistake of choosing you over all those other candidates who would likely have known better than to ask that question.