Lawful evil is the methodical, intentional, and frequently successful devotion to a cruel organized system. In 4th edition mechanics for Dungeons & Dragons lawful evil is found under the umbrella of the evil alignment.
A lawful evil character methodically takes what he wants within the limits of his personal code of conduct without regard for whom it hurts. He cares about tradition, loyalty, and order but not about freedom, dignity, or life. He plays by the rules but without mercy or compassion. He's comfortable in a hierarchy and would like to rule, but is willing to serve. He is loath to break promises, and he is therefore very cautious about giving his word unless a bargain is clearly in his favour.
This reluctance comes partly from his nature and partly because he depends on order to protect himself from those who oppose him on moral grounds. Some lawful evil villains have particular taboos, such as not killing in cold blood (but having underlings do it) or not letting children come to harm (if it can be helped). They feel these personal morals put them above unprincipled villains.
Many lawful evil characters use society and its laws for selfish advantages, exploiting the letter of the law over its spirit whenever it best suits their interests.
Some lawful evil people and creatures commit themselves to evil with a zeal like that of a crusader committed to good. Beyond being willing to hurt others for their own ends, they take pleasure in spreading evil as an end unto itself. They may also see doing evil as part of a duty to an evil deity or master.
Lawful evil is sometimes called "diabolical", because devils are the personification of lawful evil.
A tyrannical ruler who drafts the rules to suit himself, a corrupt lawyer or judge who uses the law to mask his own misdeeds, and the ruthless bosses and minions of organized crime are all examples of lawful evil characters.