Passed pawns grow stronger as pieces are exchanged because fewer defenders remain to stop them. In endgames, a passed pawn can dominate the entire position, tying down enemy pieces to blockading duties while the rest of the board favors the side with the passed pawn.
The ideal treatment of a passed pawn depends on the game phase. In the middlegame, a passed pawn may be best kept as a static threat that restricts enemy piece mobility. In the endgame, advancing the passed pawn becomes the primary objective, often supported by the king and remaining pieces.
Connected passed pawns (two passed pawns on adjacent files) are especially powerful because they support each other's advance. A protected passed pawn (one defended by another pawn) is a permanent positional advantage because it costs the opponent piece resources to maintain the blockade. The concept that "passed pawns must be pushed" is a valuable endgame principle, though timing and king position are always important considerations.