How To Rank Your Pieces
A ranking system I came up with on my own. Probably useful for newer players.
Level 0: Your piece is obstructing friendly pieces. In the diagram below both players want to move their knights. White's rook would have the open b file, and black's bishop would have the long open diagonal.
Level 1: Centralized and/or controlling many squares. In the diagram below white's knights are good. Black's are not.
Why is a centralized or mobile piece considered good if it's just hitting a lot of empty squares? The point is it will have greater chances to get to level 2 or 3. It's just a means to an end. This brings us to...
Level 2: Infiltration. The term infiltration means to post your piece in the opponent's territory. (Once it gets there it may already be level 3)
In the diagram below, the star of the position is white's d5 knight. It's in black's territory and even though it's not participating in a mating attack, or threatening any weak pawns, it's taking squares away from black's pieces, and because it's in black's camp, it has a high chance of becoming level 3 later.
Level 3: Attacking or defending a vital point. Often this means the enemy king or a weak pawn that can't move.
The quintessential example of this is rooks on the 7th rank (for white) or 2nd rank (for black)
So when someone says "find your worst piece and improve it" I think this is a good rough guide.
Also will help judge when it's good to trade a piece. If you're trading off one of your bad pieces, or even if you're trading off one of your good pieces, if your pieces that remain on the board are better than your opponent's then you're doing well.