Finding Active Squares
At the beginning of a game, we want to develop our pieces to the best squares and as the game progresses, we want to continue to improve our pieces.
When we are identifying the best squares for our pieces -- one important consideration is how active our piece will be on a given square.
To be clear, in chess, when somebody says "piece" they are usually talking about bishops, knights, rooks, and queens -- but not pawns. Bishops and knights are minor pieces. Rooks and queens are major pieces. So, when talking about active pieces, we are not talking about pawns.
Any given piece is on a scale of active and passive depending on the square it sits on and the pieces and pawns around it. A completely passive piece is unable to move to any square. A completely active piece is able to move to a maximum number of squares for its type.
If you take out a chess board and put one piece on it at a time in the center of the board, you will notice that the queen can control 27 squares and the rook can potentially control 14. While the bishop can at most control 13 squares and the knight only 8. The amount of squares they can potentially move to greatly influences how powerful the pieces are. There are other considerations. For example, a rook can more easily control 14 squares than a bishop can control 13 -- the bishop must be in one of the center squares while the rook can be anywhere on open files and ranks.
So from this, we understand that being active is largely about mobility. This also influences how much control we have over a square. Our pieces control a square if they can move to it -- even if that square is guarded.
There is another consideration to how active a piece is: how valuable are the squares the piece controls? In some games where the board is "closed" (many pawns occupy the center of the board and reduce mobility), there may be multiple squares that yield equal mobility, but not necessarily control the best squares. So we cannot just blindly consider two squares to be equal if the number of squares our piece would have access to are equal. We must remember that some squares are more important to control -- and I think in most cases this relates to where the action on the board will be.
GM Patrick Wolff takes the definition of active and passive one step further. "A piece that defends a pawn or another piece, particularly when it controls few squares, is called a passive piece. A piece that attacks another pawn or piece, particularly when it controls many squares, is called an active piece." I think his focus on attack and defense in his definition is probably an important distinction and consideration.
A final note: you may hear references to active and passive moves with regard to how a piece fulfills a defensive roll. An active defense is one that makes threats and doesn't necessarily guard a threatened piece, while a passive defense is one where a piece is forced to stand guard duty and make no threats. I believe an active defense is always superior -- although there may be times where there is no possibility of an active defense.
Study this position and notice the advantage that white has due to active pieces:
Even white's light square bishop is active because it attacks important squares and will soon control an important diagonal. Black's knights are reasonably active, but mostly, black has horribly inactive pieces. Black will lose this game.
This blog post is geared toward new players. Not that I am qualified to give advice -- I myself am not an advanced player. I merely hope to help struggling beginners.