Most simply, an anti-hero is a character that has heroic goals or results, but uses less-than-heroic means to achieve them. For example, where a true hero would likely let a villain live to be served justice, an anti-hero would probably kill the villain to put an end to things rather than risk escapes or such. An anti-hero would also be more willing to steal something than a true hero, especially if the item is necessary to achieve their goal.
The motto for anti-heroes in general is "The ends justify the means."
Another way, (my way), of looking at it is that when you write about an anti-hero you're asking "what makes a hero a hero?" What can you strip away from the classic image of the knight in shining armour and yet still have something you can call a hero. Can you take away their honesty, their sense of honour and gallantry, martial prowess, youth and good looks, optimism or hope and still call them a hero?
An Anti-Hero isn't necessarily a person that would do the opposite a normal hero would do. An Anti-Hero could also be the hero of a story, but flawed instead of smart, intuitive, and brilliant like most heros of a story would be. An Anti-Hero could be a hero that isn't all that great at everything he/she does, someone that doesn't always know right from wrong, and doesn't always say/do the best things.
House: People interest me. Conversations don't.
Foreman: Maybe because conversations go both ways.
House & Foreman: Like Thirteen.
Some people are hourglass shaped, some people are apple shaped, some people are pear shaped, some people are even bean pole shaped, but if we’re not careful we all become banana shaped. This is your gentle posture reminder. — Ranger