A sideboard is a collection of 15 cards that a player may bring to a game (often tournament) of Magic: The Gathering.
In conventional games, each player is allowed to bring 15 cards (in addition to his main deck) to the game. These cards are referred to as the sideboard. Players are not required to have a sideboard; but, if a player does have one, it must be exactly 15 cards, no more, no less. After the first and second game of a match, each player is allowed to swap cards in their deck for cards in their sideboard (aka "sideboarding"). This is a 1-for-1 swap, so both the player's deck and sideboard must remain the same size (often 60, and exactly 15). The player's deck must still be legal after sideboarding (for example, if a player already has four Llanowar Elves in his or her deck, he or she can't sideboard in two more). A sideboard counts as part of the player's deck, therefore the four per deck limit includes the sideboard. This also means that restricted cards are limited to one including the sideboard. (For example, the card Black Lotus is restricted in DCI-sanctioned Vintage Magic tournaments. This means that only one Black Lotus is allowed per deck, including sideboard, in the Vintage format.)
Sideboarding helps a player address the weaknesses of his or her deck against a certain opponent. For example, if a player consistently loses games against anyone who is playing red "burn" spells like Ghitu Fire and Urza's Rage, then the player may want to put four Chill (so as to "hose" red by increasing the spells' playing cost) or maybe four Ivory Mask (to prevent the targeting of a player) in his or her sideboard.