In Yu-Gi-Oh!, there are two separate formats that players can participate in: Advanced and Traditional. These formats determine the eligible cards that are legal for competition.
Compared to other card games, like Hearthstone and Magic: The Gathering, which have varying modes that determine a card’s legality based on its release, Yu-Gi-Oh! allows cards from the first set all the way to the present.
While this could lead to issues with design space and balance, any potential problem is remedied by banning, limiting, or semi-limiting a card that proves to be too powerful or consistent. Once a card lands on the Forbidden List, the two separate formats determine how many copies of it are allowed to be played.
The Advanced format is the main competitive format that officially-sanctioned tournaments follow. Any card that is Forbidden isn’t allowed to be put in your Main, Extra, or Side Deck. In addition, there are Limited and Semi-Limited cards, meaning that you can only have one (Limited) or two (Semi-Limited) copies of that card within any of your decks at any given time.
If a card is placed on the Forbidden Lists, it always has a chance of being removed at a later date, like Raigeki or Black Luster Soldier – Envoy of the Beginning.
While the Advanced format is considered more competitive and the healthier option between the two modes, some players still want to play with their favorite past cards and combos regardless of legality. In the Traditional format, you’re allowed one copy of any card that’s considered Forbidden and two if it’s Limited. Any cards that are considered Semi-Limited on the ban list are allotted three copies, the normal maximum that can be put in a constructed deck.
Due to the “anything goes” style of the mode and little to no tournament support, the Traditional format is considered more casual to most of the player base.
You can keep up with the current Forbidden List here. It was recently updated earlier in the month.