Hello, dear chess friends!
Before we continue with the exposition on pawns role in the endgame, it is important to give a piece of practical advice to chess coaches. Endgame theory is a vast area and it is helpful to break it down into smaller and practically meaningful parts. Especially for beginners and players who did not develop endgame routine yet, it is important to think in terms of simple guiding principles in the endgame. For example, from my own experience, I believe it is important to teach young chess students to always focus on 3 things in the endgame: 1. Creating a passed pawn, 2. Centralizing their king, and 3. Blocking or defending against opponent's passed pawns.
This is useful for young students of the game practically and methodically as well, because even if they may not yet be able to grasp certain finer points in the endgame, such as schematic thinking, they will always have in mind the bigger picture (pawns and king are important) and will therefore be less prone to making silly errors in the endgame, such as grabbing useless pawns, leaving their king "at home", not putting the rook behind opponent's passed pawn, etc.
After this small digression, I would like to proceed to the two final topics pertaining to the importance of pawns in the endgame: 1. The defended passed pawn and 2. The outside passed pawn
1) Defended passed pawn – The strength of defended pawns in any phase of the game is that they do not have to be defended by other pieces. In that sense, the ideal pawn structure is a pawn chain – a structure where pawns defend each other along a diagonal. The "Achilles heel" of the pawn chain in naturally its base, but attacking the base of the pawn chain is generally much more difficult than attacking an isolated pawn. As the number of pieces in the endgame is very limited, the weakness of isolated pawns increases and, by the same logic, the value of defended pawns increases. Let us look at a typical endgame mistake made by a young inexperienced player who did not understand these ideas.