The Trinity is a term used to refer to the trio of Wonder Woman, Batman and Superman.
While they come from different aspects of life, with different powers and methods, and entered the super hero community at different times, the three tend to dominate any setting they appear in. Other heroes immediately defer to them while Batman and Wonder Woman themselves defer to Superman.
Historically, the trio worked fine together until time frayed their morale.
Following Robin (Jason Todd)'s death, Batman turned away from hope and ceased to dream of victory over evil. Instead dreaming only of vengeance he turned fully to using rage and fear against the guilty without concern with how it may affect his comrades and the innocent.
Eventually, he was only interested in fighting to punish those that hurt others and did not answer those in aid for other reasons.
Diana's Themysciran teachings say that to kill a man in battle can be necessity, but to kill a man in chains is failure. There must always be hope; hope of redemption, hope for grace. A dead man cannot be won to truth. Believing fully in these teachings, as time went by Diana became increasingly frustrated with the corruption and impatient personalities around her and eventually gave up on hope for people to redeem themselves and turned solely to victory through strength and the warrior's way.
Superman desired to live as a human, eventually his calling as a hero and protector was transformed into a calling as a loving husband. His heart was no longer in his role as a hero but in his role as a man and he no longer set himself as an example to help others learn and grow.
By the time of the Infinite Crisis incident, the Trinity no longer had the patience to work with each other for varying reasons. Batman believed Superman no longer took his work seriously and Wonder Woman had become a simple combatant. Superman believed Batman had become a bully and Wonder Woman had become a killer. Wonder Woman no longer felt comradeship with either hero.
Following the incident, the trio recognized their failings and took a year sabbatical to reassess themselves and reaffirm their commitment to their jobs.
Superman acts as the savior; saving people from their problems, Wonder Woman works to inspire others to achieve on their own, while Batman works to manipulate people and events from the background.
Batman is symbolized by the Moon; operating at night, Wonder Woman is symbolized by the Earth; born from clay, Superman is symbolized by the Sun; the source of his power.
Batman is an "insider"; born to the world's dominant civilization but walls himself off from it. Wonder Woman is an "other"; born in the world but in a separated culture. She walks amongst humanity but holds herself apart from it. Superman is an "outsider", born to another planet but immerses himself in the world.
Batman is the Brain, Wonder Woman is the Will, Superman is the Heart.
Superman is Science, Wonder Woman is Magic and Batman is Humanity in between.
Batman represents Man of Present Day, Wonder Woman represents Woman of Ancient Myth and Superman represents Man of Tomorrow.
Batman is The Avenger, Wonder Woman is The Warrior, Superman is The Guardian.
The populace think of Batman as scary and not someone they'd want to see anywhere close to them because it means there's trouble nearby. The populace regards Wonder Woman as a benevolent warrior and a symbol of change; a notion some people find uneasy. The populace thinks of Superman as a cool big brother. Like he knows you, likes you and would never let anything hurt you.
Before the arising of Wonder Woman, Batman and Superman. The forces of virtue were led by Hawkman, Green Lantern (Alan Scott) and Flash (Jay Garrick).
The evil counterparts of the trinity are long thought to be the Joker, Lex Luthor and Cheetah (although some figure that Circe may be a better match than Cheetah).