Lawful Good are characters who believe in upholding the law and maintaining order over chaos. Lawful Good characters often never question the law and does anything he or she can to abide by it.
Neutral Good are characters who believe more in doing good rather than uphold the law, though are not against law and order. Most neutral good characters just act based on what they think is the right thing to do.
Chaotic Good are characters who are still considered heroic, but are free spirits who don't conform to law or order. Some chaotic good characters even downright hate these two things and think they do more harm than good.
Lawful Neutral are characters who believe abiding by the rules is more important than if you are good or evil. Most lawful neutral characters do not care if the rules they abide by are harmful or not.
True Neutral are characters who don't fall into either extreme. Most of the time, these characters are seen keeping balance or simply not caring. Some true neutral characters do haenous things, but never without justification.
Chaotic Neutral are characters who fail to follow into either side of good or evil. A chaotic neutral character may not commit any crimes, but they're still not very nice people. Basically, most jerks fit into this alignment.
Lawful Evil are characters who abide by cetain rules and force them upon others, most of the time being dictators, tyrants, or corrupt officials. Lawful evil characters always seem to have some position of power.
Neutral Evil are characters who act based on what benefits them. Sometimes they're on the side of the heroes and sometimes they're on the side of the villains. Most anti-heroes fit into this alignment.
Chaotic Evil are characters who are full-out psychopaths. Those who don't care for morality or other people's lives, and most of the time have no remorse for committing crimes, no matter how bad they are.