The dictionary definition of manners is "A person's outward bearing and behavior toward others." Another way of putting manners is as "the understanding and chosen expression of society's rules." Yet another way of putting it is like this: Life is a game. We are players in the game. The game has rules—some written, others unwritten. How we choose to behave in this game, vis-à-vis the rules, says a lot about what sort of players we are. Our behavior is information the other players can read to tell them if we play fair, play in a sportsmanlike way and play well.
In a nutshell, this is why good manners are important. Sure, you could have good manners out of a sense of decency, or because it is how you would want to be treated, but in the end there is a perfectly selfish reason to have good manners. Specifically, good or bad, your manners are a criterion on which you will be judged by other people, and plenty of those people will have a say in the introductions made on your behalf, jobs won or lost and the opening or closure of doors you didn't even know were there.
So ask yourself, "Do I have good manners?" Better yet, take this quiz, and we will tell you.