Train Bridge at Swarthmore College crossing Crum Creek

Alignment

Good Vs. Evil

Morality is a hard topic to cover in D&D. I view it as the fight for good and evil by the gods. Would good aligned gods agree with your actions? Would a evil god congratulate you for your pillaging?

Good
Someone who is morally good in the eyes of the gods. Willing to go the extra mile to help those around him without expecting compensation.

This does not mean your character has to personally stop all evil he witnesses. Nor do you need to donate all personal wealth to the poor. Your character needs to weigh the cost of the decisions he makes. Attacking a guard who is beating up a homeless man is not worth the jail time nor the beatings you'll receive. Working your way up through the legal system to get the guard fired may be though.

A wizard who volunteers feeding and healing the sick and disposed.

Neutral
Someone who is neither good nor evil in the eyes of the gods. Often times they are a loner or detached from the hard decisions life has to offer.

A woodsman caring for his family. He cares little for the war waging outside of his forest home.

Evil
Someone who is morally evil in the eyes of the gods. This does not mean you are Satan incarnate and have to kill every kitten or orphan you see. This often manifests itself as power or authority complexes.

A guard who collects bribes in exchange for "protection" from the local gangs.

Lawful Vs. Chaos

I can't sum it up better then what the books say. Source can be found here.

Lawful characters tell the truth, keep their word, respect authority, honor tradition, and judge those who fall short of their duties. Chaotic characters follow their consciences, resent being told what to do, favor new ideas over tradition, and do what they promise if they feel like it.

Lawful
Law implies honor, trustworthiness, obedience to authority, and reliability. On the downside, lawfulness can include closed-mindedness, reactionary adherence to tradition, self-righteousness, and a lack of adaptability.

A trader more interested in money then the going ons in the land.

Neutral
Someone detached from society would be considered Neutral. While they aren't driven to rebel they have no compulsion to help others.

A ranger uninterested in city life lives in the woods living off of wild plants and whatever he can hunt.

Chaotic
Chaos implies freedom, adaptability, and flexibility. On the downside, chaos can include recklessness, resentment toward legitimate authority, arbitrary actions, and irresponsibility.

A warrior fighting to overthrow his oppressive government.