The idea
If an opponent is probably ready and your hand is far from winning or low in value, the expected cost of feeding them outweighs your chance of winning. Folding means discarding the safest tiles available instead.
Safe-tile ranking
Against a riichi in Japanese play, tiles in the riichi player's discards are completely safe due to furiten. Tiles others have discarded after the riichi and the player passed are also safe. Then come honours with several copies visible, and suji-based reads.
Keeping safe tiles
Strong players often hold one or two safe tiles in reserve during the middle game, so they can fold without breaking their hand into dangerous pieces.
Partial defense
Sometimes you can continue toward a hand while avoiding the most dangerous discards. Judging that balance is the essence of "push or fold" decisions.
