The Trinity in the TCG and OCG consists of the following three cards:
These cards are known as such due to their ability to allow the Turn Player to gain massive Card Advantage. In fact, they are banned in the Advanced Format for this very reason.
The other "Trinity" is a set of three spell cards that, if all three were in your opening hand, would cause the opponent to start with only one card in their hand (two after they draw their first card in their turn). This makes the turn player that draws them gain massive advantage. The first card of this "Trinity" to get forbidden was "The Forceful Sentry with the April 2005 Forbidden List. In September 2007, the last card of this "Trinity" (Confiscation) was put on the Forbidden List.
In the Anime and Manga, The Trinity refers to "Kazejin", "Suijin", and "Sanga of the Thunder", which are the three monsters needed to summon "Gate Guardian". Later on it was used to refer to "Obelisk the Tormentor", "Slifer the Sky Dragon", and "The Winged Dragon of Ra", also known as the "Egyptian God" cards.