It is almost impossible to imagine a story without some kind of unifying objective. In most stories this is easily accomplished with a Big Bad Evil Guy (BBEG). Even if your Big Bad isn't a person &/or creature, one still demands a replacement Thoroughly Nasty Thingy as the main problem. This Nastiness could be some inclement weather, an unexpected virus, a complete set of animated brooms that don't accept new orders - or even the onset of someone's conscience. Sometimes this Nasty Thingy is not so nasty ('the need to climb a mountain... because, um... it is there?') - whatever it is, that unifying objective allows hero the ability to be heroic. Without this Often Evil Unifying Objective, any hero is out of a job.
As stories simplify life, games simplify stories. The game D&D requires that 'Black Hat' characters are obviously bad and painted with a broad philosophical brush. You recognize them when you meet them / you don't feel bad when you kill them. An example: say your hero slaughters a whole encampment of raiders like animals - killing the women and children too. As long as these raiders are obviously evil, all such murder is okay and your hero is not going dark on you. The Alignment System is slightly more complex than this, but not much. In fact, in early editions of D&D, there was magic that would allow you to know who was good and who was bad. A holy warrior or 'paladin' had a special detect-badness sense - they could slaughter tens of thousands without ever having to slow down. "Is genocide bad? No, of course not!"
The D&D game system has official rules on dividing all creatures into nine ethical-moral slots. Over time these ideals became stereotypes that further degraded into memes. Below are brief (albeit ridiculous) summations.
Chaotic Good: Freedom is really important! Go with your gut - and keep collateral deaths to a low(ish) number. "We are here for a good time, not a long time!"
Lawful Good: The law is good and the Good must obey the law! Often played as 'lawful stupid', characters of this alignment told everyone what to do, usually with more arrogance than folks from an Animal Rights / Vegan Convention. "I am the law and i am the way!"
Neutral Good: Be nice. "Why can't everyone just... get along?"
Chaotic Neutral: Give 'totally random' a try. Many players choose this alignment so they can do really stupid things for no apparent reason? 'It is what my character would do!'
Lawful Neutral: This alignment tends to be given to stoic-stuffy bureaucrats and guard captains just days from retirement. These people are not fun at parties.
Neutral: This alignment is for beasts and monsters of no intelligence. Ironically, it was also given to the wisest of druids that sought a perfect balance between all ethics, religions, attitudes, nature, and society.
Chaotic Evil: Notoriously the 'kill everything' alignment. Even with 30 in intelligence and wisdom, creatures with this ethos-tag seemed to be slaughter-obsessed.
Lawful Evil: Traditionally given to more intelligent monsters that are contract-needy / power-mongers. Most expected those of this alignment to be unable to lie.
Neutral Evil: Stereotypically these guys did everything in their power to screw you over.
Vork Doxikk the Vexed (orc / chaotic EVIL): Vork leads a large war band. He secretly has a book (!) from an orog-orc friend called: "Tried & True Tactics - Survival Strategems". Though Lord Doxikk presents himself and his leadership as both chaotic (and evil), his battle-plans are not chaotic at all. Vork knows full well that his orog advisor is smarter, wiser and more objective. Even if Vork cannot understand it, he follows his orog-orc's advice &/or book to the letter.
Shanky the demonling (fiend / chaotic evil): Shanky has been summoned, captured and bound over centuries, serving lawful wizards via soul-binding magic. Shanky had many excellent experiences serving these wizard masters. In contrast with this, his fellow demons on his home plane(s) have always betrayed him as they seek to succeed with Abyssal politics. As a result he passionately hates all demons. He seeks to cause great suffering to fiends and has become quite skilled at hunting / killing them. He otherwise presents as warm, friendly and adorable to any creature from the prime material planes - especially if they will help him wreak havoc on demon-kind.
Aluri'astraœx Of Auspice (green dragon / lawful evil): Green dragons collect sentient creatures as treasure. Unlike gold, sentient creatures (like 'humans') don't live that long and tend to kill one another a lot. As a result, Aluri seeks followers that are lawful &/or good (as possible) - so that they work together and accumulate more 'treasure'-followers for her. Should anyone seek to give her advice, 'assist' or interfere with her expansive rulership in amy way (even if they are angels, lawful good paladins, metallic dragons, demi-gods of healing, etc.), she will destroy them. Yet, for all intents and purposes, she is extremely loving to any who faithfully follow and serve her.
Radiant Vauriel of The Highest Celestia (angel / lawful good): Vauriel has been corrupted by the demonic forces she has been slaying for thousands of years. Covered in too much bad blood, spending too much time amid piles of demon bodies - it has taken its toll. She should have gone back home, even to take a break. Now this warrior angel takes her destruction far too far. She will gladly slaughter any who deviate from the strict laws in her Codex Of The Guard, a worn and faded book she was given centuries ago.
Krazz'sh da Krash (ogre / chaotic neutral): Krazz'sh was hired on as a mercenary by a group of dragon slayers. He was given armour (well, more 'barding' really) some amazing weapons, a well-made shield, lots of food (spiked with Goodberries so he can be fed at a reasonable cost-efficiency) and more. He loves his friends and is also responsible for taking care of his adopted home town between dragon-hunting missions. He is, in his home town, a law abiding citizen right down to paying taxes (he has a trustworthy accountant for this). Still, whenever he is out of his home terrain he is a bit like a cat leaving a house: he goes quite feral to everyone except his own adventuring party.
This effectively takes the two dimensions of alignment (good-bad / random-conformity) and adds three other dimensions to them:
If you or your players find this confusing, you can simply write out the alignment as a vague influence and write out the Big Three: 'Where are they from', 'What do they want' and 'What are their plans'.