Furiten in riichi mahjong is a state in which a player has discarded a tile that would have otherwise completed his hand. A player who is furiten cannot win on an opponent's discard, but can only win by self-drawing the needed tile. This rule is the crux of riichi mahjong. This is why all discards and melded sets are organized to show ownership the tiles discarded.
It is a common misconception with beginners that being furiten only applies to discarding the winning tile or a yaku-completing tile. This is true since the winning tile is also a tile a tile that can complete his hand, furiten, however can taken on other forms.
Example 1
Wait(s): 3-bamboo.
The player is aiming for Pure Straight as his yaku.The player is furiten if he has discarded 3-bamboo at any point.
Example 2
Wait(s): 1-bamboo, Green Dragon.
The player is furiten if he has discarded 1-bamboo even if it is the Green Dragon that he is waiting on to complete his yaku.
Example 3
Wait(s): 1-character, 3-character, 4-character.
This player is going for All Simples. The player is furiten if he has discarded any these tiles that would have otherwise completed his hand. Even if he discarded 1-character and was going for All Simples he would still be furiten.
Temporarily Furiten
A player who forgoes claiming a discarded tile that would have completed their hand (even if it yields no yaku), is temporarily furiten until the next go-around (the next time they draw a tile). If the go-around is interrupted by a chow, pung, or kong the player is no longer furiten. Note that a player who has previously declared riichi and then chooses to pass on another player's discard that would have completed their hand (even if it yields no yaku) is rendered furiten for the remainder of the hand and may only win via self-draw. Being temporarily furiten only applies to players who have not declared riichi.
Example 1
Player C is going for All Simples.
Player A discards 1-character; Player B in turn discards 4-character. Player C cannot win on the 4-character, because the 1-character was discarded within the same go-around.
Penalties & Errors
A player who calls on a winning tile while furiten commits a foul called a chombo.