Why add a minor to a PhD? As an undergrad I had a couple majors and a couple minors...no big deal. Ultimately all it meant was I took a lot of classes all over the place and went through the time and effort to declare them.

As a PhD student, though, declaring a minor is pretty uncommon. Hell, a lot of schools don't even offer the option. My understanding is that minors are usually for highlighting a certain amount of coursework in a closely related field to the one you're studying. Seemingly obvious pairings would be a PhD in Math with a minor in Statistics, or a PhD in Classics with a minor in Philosophy. However, unlike in undergrad (and really even at the Masters level), during a PhD the emphasis is primarily on research, not coursework. So why is a PhD minor a thing? Does it serve any purpose more than just another notch in your academic belt?

Personally, I am thinking about adding a Math or Statistics minor to my PhD in Computer Science, but I can't come up with a good reason other than "I'm interested in higher level math/stats and it's really applicable to the area of CS I work in." That's enough to satisfy me, I guess, but is there really any other reason to do this?

EDIT: I guess I should add that *in my case* I'm not thinking about a minor for minor's sake, but rather that I'm already taking a bunch of courses in that area so it just means an extra course or two. The question still stands though: why is it a thing? And, furthermore, does it carry different connotations in different areas (e.g. the humanities vs. applied sciences)?
A minor gives a grad student the option of diversifying his/her learning experience. Much research is interdisciplinary (like stats and CS), so taking a few classes in another department can be very beneficial. It also gives a grad student an excuse to take courses in something that isn't directly related to their research. (Minoring in a foreign language or business can be generally useful, for example.) In my own experience, most grads minor in something closely related to their research. 

As far as I know, very few people look at a graduate student's minor. The biggest reason I can see for having a minor outside one's home department is to diversify one's educational background. 

I looked around to see what universities said about this. Georgia Tech states that "The purpose of the minor is to encourage a wider interest on the part of the student and to provide a broader basis for the evaluation of the student's capabilities." (source) Stanford requires a minor for its Education grads (source).