The D&D Alignment chart is a system designed to measure the morality of an individuals actions and motives. It is a chart with 2 axis, good vs evil, which measures how much a charter values human life as opposed to sacrficing others wellbeing, and law vs chaos, which concerns how a charterer feels about rules and order, as opposed to personal freedom and individualism.
PLEASE NOTE: This is not a place to post where you think ideologues/people fit on the alignment chart. Instead, feel free to start you're own here.
Lawful Good
A lawful good character follows a code that involves taking responsibility for trying to help others. This can be the code of there society, group or just there own personal code. They will tell the truth, speak out against injustice, and try and make sure people get what they deserve, while still maintaining a sense of mercy. They think order is important to make sure people live safe, orderly lives.
Neutral Good
Neutral Good characters try and do what they believe is right, viewing codes and the laws as a means to accomplish these ends. They'll work with authorities when it's pragmatic, but don't feel beholden to them.
Chaotic Good
Chaotic good characters are those who value freedom, not only for themselves, but for everyone. They tend to go with there guts and do whatever they feel like, it just so happens that most of what they feel like doing involves helping others. They hate bullies and people who try and force others to fit a mold or who try and tell them how to live there lives.
Lawful Neutral
Lawful neutral charters act based of laws, tradition, or there own moral code. They view flowing these rules as more important then trying to help individual people or furthering there own self interest, for the good of society as a whole. They may view there ideals as something which everyone should follow, or they may view at as just for themselves.
True Neutral
A true neutral character isn't really devoted to Law, Chaos, Good, or Evil. They mostly do what they think will benefit them and those close to them the most, while being unwilling to cross certain lines, like torturing or killing people. A minority of true neutral characters view neutrality as a good in and of it's self, seeing favoring any other alignment as a dangerous bias.
Chaotic Neutral
A chaotic neutral character will strive to protect there own ability to do whatever the hell they want. They don't tend to actively antagonize lawful intuitions, because they don't really care about anything that doesn't immediately affect them. They do however, tend to run into conflict with others as a byproduct of their actions.
Lawful Evil
Like the other lawful alignments, a Lawful Evil character still has a code or set of rules they obey. However, unlike those other alignments, that doesn't stop them from doing and supporting awful things. They may think that the only way to maintain order is through brutality, they may be devoted to a code that just so happens to allow them to be awful to everyone around them, or they may even be an active crusader for tyranny. Regardless, they tend to view hierarchical structures as the natural order of tings. As such, while they don't really have a problem serving those who they view as above them, they look down as those beneath them.
Neutral Evil
Neutral evil charters are out for themselves, pure and simple. They have basically no qualms about who they hurt in getting what they want, and will be willing to work with others if they have something to offer them.
Chaotic Evil
Chaotic evil characters do what they want, when they want, and damn the consequences. They get some kind of sick thrill out of hurting other people, and follows whatever destructive whims they might have at the moment. Whatever groups or plans they might make tend to be short lived and poorly organized, so even though they tend to be the must destructive alignment, they don't tend to succeeded as often.