A sideboard is an optional group of cards which a player can use to modify their deck. This is done by removing cards from their sideboard and using them to replace cards in their deck. The cards from the deck are then placed in the sideboard, to be switched out again later if desired. Any restrictions on deckbuilding for a tournament also apply to the sideboard (if any) for that deck.
In Constructed events, you may only exchange cards between your deck and sideboard between games in a match. You may not sideboard between matches or before the first game in a new match; you are required to "unsideboard" after every match, effectively resetting your deck to the way it was at the beginning of the tournament. The size of your sideboard must be exactly 8 cards. You may include additional cards that you do not intend to actually play to meet the 8 card requirement.
In Limited events, you may sideboard in between matches and in between games in a match, but not after pairings for the new round are announced. Your sideboard consists of any card in your limited card pool that was not used to construct your deck. Unlike constructed events, you are not required to swap on a 1:1 basis. For example: while sideboarding, your limited deck may go from 30 cards to 40 cards, as long as your deck continues to meet any and all construction rules for that event.