The Extra Deck, formerly known as the Fusion Deck, is a pile of Cards where Fusion, Synchro, XYZ, and Link Monsters (as well as Pendulum Monsters that would otherwise have been sent from the field to the Graveyard) are stored during a Duel.
During a Duel
When a Duel begins, you have to place your Extra Deck face-down in the Extra Deck Zone of the field. Like the Main Deck, the number of Cards in the Extra Deck is public knowledge. Unlike the Main Deck, a player may look through their own Extra Deck at any time. The face-down contents of the Extra Deck are not public knowledge, so a player may not look through face-down Cards in their opponent's Extra Deck; however, the face-up Cards in the Extra Deck are public knowledge, so either player may look through them at any time.
Cannot exist in the Hand
If a Fusion Monster, Synchro Monster, XYZ Monster, or Link Monster would be returned to the hand or Main Deck, it is instead returned to the Extra Deck (face-down), since Fusion Monsters, Synchro Monsters, XYZ Monsters, and Link Monsters cannot exist in the hand or the Main Deck. You don't have to shuffle your Extra Deck, even when a Card specifies that the Card would be shuffled into the Deck.
Extra Monster Zone
Monsters that are Special Summoned from the Extra Deck must be Special Summoned to a Main Monster Zone that a Link Monster points to or the Extra Monster Zone. (Before the introduction of the Extra Monster Zones with Master Rule 4 in July 20, 2017, a Monster could be Special Summoned from the Extra Deck to any Monster Zone.)
Extra Deck Construction
During Deck construction there can be, at most, three Cards with the same name in your Main Deck, Extra Deck, and Side Deck combined. The Extra Deck has a maximum size of 15 Cards (including all Fusion, Synchro, XYZ, and Link Monsters). However, Pendulum Monsters placed face-up in the Extra Deck during a Duel can cause the total size of the Extra Deck to exceed the maximum size permitted during Deck construction.