An active king is a king that participates directly in the game by moving toward the center or the opponent’s pawns to exert concrete pressure on the position.
In the endgame, the king is no longer a piece to be sheltered at all costs — it becomes a full participant, capable of attacking pawns, supporting its own, or controlling key squares. A passive king in the endgame often allows the opponent to convert an advantage without resistance. For instance, in a pawn endgame, a king placed in front of its passed pawn is frequently enough to ensure promotion, while a distant king can do nothing to stop it.
In practice, as soon as heavy pieces (rooks and queen) are exchanged or the position simplifies, immediately look for the best central square for your king and advance it without delay. Every tempo lost leaving the king on its back rank can cost the game.