The Triforce is a sacred item that appears throughout The Legend of Zelda and frequenty acts as a logo for the series.
The Triforce first appears in the seminal The Legend of Zelda, though only the Triforce of Power and Wisdom make an appearance. The Triforce of Courage debuted in Zelda II: The Adventure of Link, and the pieces have appeared as a trio ever since. While the Triforce has not appeared in every Zelda game, the games that do feature it have the three pieces spread across the main characters - typically the blood of the goddess holds the Triforce of Wisdom, the left piece; the reincarnation of Demise holds the Triforce of Power, the top piece; and the spirit of the hero holds the Triforce of Courage, the right piece. Wielders of a Triforce piece are considered incredibly powerful individuals, capable of seemingly impossible feats and abilities.
If all three pieces are brought together, the Triforce grants the wielder a wish. However, the Triforce can deem someone as not worthy of a wish. In this case, the pieces split apart, with only the piece that most closely represents the wielder staying with them, and the other two choosing on a host of their own. A wielder can be identified by a triangular mark typically seen on the back of their hand. The Triforce does not discern between good and evil, so anyone can theoretically wield the Triforce and have their wish granted if they are deemed worthy. This is most clearly seen by Ganondorf, the most reoccuring antagonist in the series, being chosen by the Triforce of Power despite his malicious intentions in all of his appearances.
Also, the Triforce is not indestructible and can be broken, an example being in The Legend of Zelda where the princess shattered the Triforce of Wisdom into eight pieces and the only way to repair it is to bring all the pieces back together. There are even instances of the Triforce itself showing a level of sentience, such as deciding if a potential wielder is worthy and the essence of the Triforce telepathically communicating with people of rare occasions. The Triforce is considered the ultimate power in the land of Hyrule, to the point that several wars have broken out over use and custody of the Triforce, and it has been separated and hidden on multiple occasions out of it simply being too powerful for average people to get their hands on it.
In the Super Smash Bros. series
The Triforce appears as the symbol of The Legend of Zelda series in all five Smash Bros. games. In the opening movie of Super Smash Bros. Melee, Link's, Zelda's, and Ganondorf's arms appear, with each of them wielding their respective piece of the Triforce. It also appears as structures on Zelda and Sheik's Target Test stages, and in the Underground Maze of Melee's Adventure Mode as a goal one must reach to complete the stage. In Super Smash Bros. Brawl, Super Smash Bros. 4, and Super Smash Bros. Ultimate, the Triforce is seen in Link, Toon Link, and Young Link's Final Smash, Triforce Slash, as it traps the opponent while Link, Toon Link, or Young Link slashes them. In Super Smash Bros. Ultimate, Zelda uses the Triforce of Wisdom in her new Final Smash, where she traps the opponents in the titular piece of the Triforce. Additionally, the Animal Crossing Triforce amusingly appears as one of the various items thrown into the house as it's being built in Dream Home.