Neutral evil is one of the nine alignments in Advanced Dungeons and Dragons. The game's 3rd edition Players Handbook calls the neutral evil character a "malefactor." He is out for himself and will kill, rob, or maim anyone if it advances his interests. This alignment is also known as true evil.
The neutral half of the alignment refers to the character's disposition towards law and chaos. She does not tolerate the constraints of law, tradition, stricture, or creed, nor does she abide indiscriminate barbarity. She is out for herself, so when law and order suits her needs, she tolerates it. But she leaves the door open for herself to rebel should the walls start closing in on her. Circumstances and self-interest decide.
The evil half of the alignment refers to the character's attitude towards his fellow man and the common good. It is not that the evil character necessarily does not care about others or does not value life; he just cares about himself and his own life above everything else. He will not run into any burning buildings to save someone, unless that person is amazingly wealthy and is wearing a fist-sized diamond around his neck. And before that, he'd ask the dwarf in the party how much heat a diamond can tolerate.
Thus the combination of these two elements -- indifference towards law and chaos plus evil -- produces a soul entirely bent on self-preservation and self-interest without conscience. Therefore, neutral evil is a good alignment for a thief or assassin character, as the mercenary nature of those classes satisfies the self-interest aspect. Do not let a neutral evil character walk in the back of the marching order, nor let this character stand watch alone.