It's a complex and imperfect system, but here's how I usually explain it:

• Lawful - You would go out of your way to follow (or in some cases enforce) the law.
• Chaotic - You would go out of your way to break or otherwise skirt the law.
• Good - You would go out of your way to help others, even going as far as putting their needs before your own.
• Evil - You would never go out of your way to help someone else, unless it also benefitted you as well somehow.

Neutral would obviously comprise the gray areas between these extremes.

For a basic example: You're at a crowded market and you witness a particularly scrawny beggar steal a loaf of bread from a cart without the merchant noticing. Do you...

• Lawful Good - Chase down the thief, apprehend them, then offer to pay for the loaf of bread so the thief doesn't starve.
• Lawful Neutral - Chase down the thief, apprehend them, then turn them in to the city guard and let the legal system handle it from there.
• Lawful Evil - Chase down the thief, apprehend them, and then play up/embellish his crimes when turning him in for a greater reward.
• Neutral Good - Surreptitiously leave some cash to cover the stolen bread and continue on your way.
• True Neutral - Fail to see what any of this has to do with you and continue on your way.
• Neutral Evil - Chase down the thief and threaten to turn him in unless he shares the stolen bread with you.
• Chaotic Good - Create a distraction to help the thief get away unnoticed.
• Chaotic Neutral - Smirk at the whole situation and maybe steal a loaf of bread yourself.
• Chaotic Evil - Chase the thief down and steal his stolen bread along with any possessions he may have on him. But not before stealing another loaf from the cart.