A tournament is a competition, in which Magic: The Gathering players assemble to play the game. There are set rules for "official" tournaments, for example, only legal cards from offical decks may be used.

List of official tournaments

Friday Night Magic
Friday Night Magic (FNM): Many local game stores hold these tournaments on a weekly basis. These are usually fairly casual, often Standard Constructed, and are a good place for less experienced players to acclimate themselves to competitive Magic. As a DCI sanctioned event, FNM events require a valid DCI number to participate. Incentives for participation include planeswalker points and achievements. Physical prize support is another feature of FNM events, with the top player(s) receiving promotional cards- foil alternate artwork versions of previously printed cards. Some stores offer additional prize support per the owner's 

Mtg prerelease
Prerelease/Game Day events

These events are held in accordance with the release of new sets, with prereleases a week before the set's official release and Game Day being held a month after. These events may vary in size but are not unlike a larger FNM. Prerelease events are conducted as Sealed pool events, meaning that each player gets a set quantity of sealed product and builds a deck out of the cards they receive. Game Day events are usually Standard Constructed format. Both events usually feature better prize support than FNM events, including playmats and booster packs/boxes. Game day events also feature alternate (full) art promotional cards as participation prizes and foil full alternate art cards as top cut prizes.

Mtg qualifier
PTQ (Pro Tour Qualifier)

These events are usually medium sized tournaments, run in Standard or Modern constructed. Higher-caliber players typically play in these events and they are more strict in regards to rules. Winning a PTQ event qualifies a player to compete in the pro tour, a very prestigious and elite tournament series where the world's best players face each other with serious prizes at stake.

Grand prix
Grand Prix

These events are large and run for multiple days. They are the largest events open to the public and may be run in almost any DCI format (Standard, Block Constructed, Modern, Legacy) and are typically a number of rounds of constructed followed by a draft for the top cut. Side events are conducted as well. GP events feature cash prizes, foil promo cards, pro tour invites and other valuable prizes for top players.

Mtg protour
Pro tour and National/World championship

Magic world cup
World Magic Cup