NOTE: This will be a slight departure from their origins in attempt to explain the characters to mainstream audience.
2014 Film Slate
Wonder Woman
This film's opening credits and beginning explain how beings from another[more technologically/socially advanced] dimension called Olympus visited Earth around 800 BCE. These visitors were worshipped beacuse of their divine powers. They were called Gods, and were responsible for why Greece became a powerful civilization. However, the Greeks became too reliant on the gods and took them for granted. The Gods decided to return home to their Olympus and their abscense led to Greece's downfall as a civilization.
A group of Spartan and Athenian women wished to escape the Peloponnesian War (A war between Athens and Sparta) and so they ventured to an island and colonized it, calling it Themyscira. The citizens thrived on Thymscira independently, and The Gods returned. Their relationship with The Gods was better than ever and for centuries there was a golden age for Themscira and its inhabitants (Artemis and Athena even granted the Amazons immortality). Until Zeus had a child out of wedlock to Queen Hippolyta of Themyscira. Zeus' wife was enraged and severed ties with Themyscira. This demigod child was known as Diana (Daughter of Zeus/ Wonder Woman) and is endowed with: super-strength, flight, super-durability, super-speed, longevity. She is trained to be a warrior (like the other Amazons) from a young age and is worshipped like a goddess (since she is the closest thing to The Gods that they have).
Diana grows curious about the outside world and Hippolyta tells her that Themyscira used to trade with an underwater civilization that the Gods had introduced them to. Hera's (Zeus' wife) disdain for Diana grows and she sends Ares to kill her. Ares fails to kill her, and notices she is a great warrior. He gives her the following enchanted weapons/armor: Lasso, Sword, Tiara, and Wrist armor. The Gods accept Diana and allow her to rule Themyscira
Aquaman
Beginning- Poseidon builds an underwater city after he loses Athens to Athena, and allows the Greeks to reside in his city. Poseidon fathers a child with one of the human women, and she is made Queen of Atlantis. The descendants of Poseidon are inbred and rule Atlantis as a monarchy. The Atlanteans thought inbreeding would preserve his divine traits. But, the lack of genetic diversity meant they could no longer survive on land for extended periods. Their technology surpasses anything else on the planet and like Themscira they have little interactions with the outside world.
As centuries pass curiousity grows, and a rebellious Atlantean Queen named Atlanna ventures to the surface world. She returns to the surface world frequently and quickly falls in love with a surface dweller named Tom Curry. Her son is named Arthur Curry and since he is a descendant of Poseidon he is endowed with certain abilities: super-strength, super-durability, able to live underwater, and communicate with aquatic life.
Arthur Curry is returned to Atlantis and groomed to be a successful king. He is trained in combat as well as educated by Atlantis' greatest instructors. When his mother dies due too to much exposure to the surface world, the royal advisor Vulko becomes his guardian
Arthur is a good king and Atlantis prospers under his tutelage , one day while patrolling the borders he notices a cruise ship sinking further and further below the surface. Arthur springs into action swimming at topspeed to the vessel and lifting it overhead while swimming to the surface at top speed. This heroic act turns a lot of attention toward him and Atlantis. The US Military wants answers and deploys a covert Navy SEAL Team codenamed: The Black Mantas to investigate the "Aquaman". They are outfitted with high tech weaponized armored wetsuits from Lexcorp. When the soldiers encounter a large shark that attacks them, they are ordered to attack Atlantis. Before Arthur can lead the Atlantean Army into battle Vulko hands him a weapon that every king of Atlantis used before him. The magical trident that was gifted to them by Poseidon. The trident allows him to manipulate water.
A massive battle takes place with Atlanteans, Great White Sharks, and Octopi VS The Black Mantas. This fight is one sided and the soldiers are killed graphically. However, one soldier remains and proves to be a formidable foe taking out Atlanteans and aquatic animals left and right. Only one Black Manta remains (he was the leader of the SEAL team). His fight with Aquaman is epic but ends with the trident impaling him.
Aquaman returns to a kingdom that is outraged by the fact that he let the humans discover Atlantis.
END CREDIT SCENE: Black Manta resurfaces on a beach swearing revenge on Aquaman.