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.