Neutral, as it pertains to Good vs. Evil, is a slightly more delicate subject, surprisingly enough, than its companion. The reason for this is that most people treat this aspect of neutrality as an excuse, much like chaotic, to do whatever they want (and, indeed, Chaotic Neutral characters tend to be at least as bad in-game as Chaotic Evil). Neutral, in this aspect, means you have no strong inclinations toward good or evil. You care about yourself, but you care about others just as much. Or, maybe, you don’t care about yourself and you don’t care about others. Or, perhaps, it just doesn’t matter.
Note: Unlike what the Players’ Handbook says, I highly doubt a Neutral-aligned character cares whether their neighbor is Good-aligned or Evil-aligned. In order for them to care, Good and Evil would have to have some definition that they’re not supposed to have in this context.
A paladin and a blackguard are fighting over a region. The paladin wants to keep the people in the area free from tyranny while the blackguard is looking to expand his power. The neutral aligned ranger watching from the hedge doesn’t join in because it doesn’t concern him. Or, perhaps, he joins in to help one side achieve his goals over the other. He might even kill them both with poisoned arrows.