Apparently Martin has said that the Others are like a distinct species, with their own motivations and such. In which case, perhaps he'll flesh them out a bit more. I seem to recall that there's a legend about the Night's King having been seduced by some female creature, and turned into what he now is, but I can't recall what the source of that is.
Within the show, I think they handled him basically fine. I think of the Night's King as a force of nature, or like a computer program that got out of control. The Children of the Forest, in the middle of their war with the First Men, took one of the First Men and made him into a White Walker (the Night's King) to fight the First Men. Apparently he did that, but also was pissed at the Children, and so fought them, which caused the Children and the First Men to band together and fight the White Walkers, managing to defeat them.
Since that time, the Night's King has sought to destroy all living things, basically because he's following his program, but expanding upon it.
Now, maybe there's a deeper story there, one of love betrayed perhaps, or something else, but at the end of the day, the show wasn't ever really about that. What the show made interesting was not the big mysteries behind the White Walkers, but rather the way that the humans respond to their threat.