"Sideboard" is an optional deck consisting of between 0 to 10 cards separate from the player's main deck to be used in a tournament. Between games 1-2 and 2-3 of each round, players may choose cards from their sideboard and swap them with some cards in their main deck. They must return the changed cards to their correct decks, to the way both originally were, before each new round.
The "4-per-deck" rule applies as a whole, thus you may only have up to 4 copies of a same card between your main deck, sideboard, even Lost Deck. Also, the sideboard can only contain cards allowed by your flag card, and the Buddy monster chosen cannot be changed between games.
The sideboard's main advantage is that it allows the player to have access to situational cards that only work against certain kinds of decks without having to keep them in the main deck, only bringing them when they are necessary (for example, a card that forbids Move). It also allows the player to adjust their decks between rounds if they feel certain cards weren't that useful against the current opponent.