The rule
If any tile that would complete your hand is among the tiles you have discarded, you are furiten and may not win by ron (on a discard). It applies to all your waits: if you wait on 5 and 8 dots and have discarded a 5, you cannot ron on an 8 either. You may still win by self-draw.
Temporary and riichi furiten
If you pass on a winning discard — by choice or by not noticing — you become temporarily furiten until your next turn. If you are in riichi and pass on a winning tile, you remain furiten for the rest of the hand.
Why the rule exists
Furiten guarantees that tiles a player has discarded are safe against that player. This gives everyone reliable information for defense: against a riichi, discarding tiles the riichi player has already thrown is completely safe.
Using it in strategy
Before calling riichi or choosing a wait, check that none of your waits is already in your discards. When defending, start with tiles in the attacker's own discard pile, then tiles discarded by others after the attacker's riichi.

