1. Yu-Gi-Oh is a card-game/show that tries to get in on the markets created by games such as Magic: The Gathering and Poke`mon. There are essentially three types of cards in this game: Monsters, traps, and magic (the latter of the two are nearly indistinguishable from one another). Comparitively, Magic: the Gathering has creatures, sorceries, lands, instants, enchantments, artifacts, and then various sub-types.
When a card is played, it stays face down on the table until you either confront it with something, or the owner chooses to flip it. Essentially, the game comes down to having the biggest, meanest, and (obviously) most expensive cards you can get for you deck. This game is about as complex as Pokemon, and that is a pretty sad thing.
2. The show the card game is based upon. Many claim that the dubbing ruined it- just like everyone claims every other anime show.
The premise of the show is basically Yugi's grandfather is captured by the evil Pegasus, who wants to unluck the power of the millenuim pieces and cards. So Yugi, who has a pyramid necklace called a "puzzle," sets out with his friends to Pegesuses island to enter his card competition. He then beats people in impossible situations using his puzzle to turn into his taller, deeper voiced alter-ego. Depite the fact that he's twice as tall as midget-boy Yugi and has a easily distinguished voice, the other characters remain ignorant of the change. He then wins by places his trust in the cards and lectures the people he beats about how they don't believe in their cards or treat them right. In other words, it's the same recurring theme from Pokemon.
The further the show progresses, the more ridiculous it becomes with it's Egyptian pharoh thing and the recent "God-cards" (further alienating those who don't have or refuse to spend large sums of money to buy those cards).
Don't believe what fans say: this is, essentially, Pokemon all over again- just with darker looking monsters.
Now the Yugi-fans are going to get me...