It's about control of the dark squares : they say black is weak on dark squares because his control of those squares is weak. When the last defender (Be7) is traded, the d6 square, no longer under control, can be used by the Knight.
Should a black pawn be on c7, the dark squares wouldn't be that weak.
I find this concept convenient, but it's only a concept. You're not bound to use it, and you can replace it by other concepts you find easier to use.
White has a weakness on the dark squares. White dominates the light squares. You hear such things all the time. Generally, I get it. But, also generally, I think it's wildly overstated/overplayed by commentators.
Square color is, of course, relevant to bishop play. But queens and rooks don't care about square color. Pawns can control color complexes, if the structure is right, or can be blockaded so as to create a bad bishop for the opponent, but there again what we're really talking about is bishop play. With respect to pawns controlling color complexes, if all bishops are off the board, I don't see why that really matters. Knights control squares of the color opposite to the color of the square they sit on (knights on dark squares control/attack light squares and vice-versa). But knights jump around and aren't limited by square color. So, again, talk about color complexes seems relevant mainly (only?) to the bishops.
But commentators talk about control of, or weaknesses on, colors as though that alone provides the explanatory key to a position. Let me give you an example. The position in the following diagram arose after 20.Bg5! ('!' given by Raymond Keene) in Petrosian-Smyslov, 19th USSR Championship, Moscow 1951.
Here's what Keene/Simpole (in Petrosian vs. the Elite: 71 Victories by the Master of Manoeuvre, 1946-1983) say (they also discuss the possibility of 20...f6, but it's not relevant to my point): "The weakness of the dark squares is suddenly highlighted, and d6 becomes a prime target for the white knight."
The comment is given as though dark-square weakness explains everything. When I look at the position, yes, I see that Black's pawns are (with one exception) on light squares, and that Black's light-squared bishop is consequently somewhat restricted. However, I also see that Black's light-squared bishop problem isn't immediately relevant to what's happening in the game. I also see that Black has a few options for freeing his bishop. I see that White's move attacks a defender of d6 and pins the dark-squared bishop to the rook. I can see that d6 would be a nice square for the white knight. It's deep in the enemy camp, and sitting there the knight would control a whole mess of squares around the black king. What I don't see is how 'the weakness of the dark squares is suddenly highlighted'. What's highlighted is that Black has a cramped position and that White is about to cramp it further.
Rather, it seems to me that saying 'the dark squares are weak' is merely shorthand for the more detailed explanation I just gave. The problem is that it's not good shorthand. It's a compressed explanation that fails to explain anything, unless you can work out the details for yourself. An equally compressed, but more explanatory, statement would be: 'White attacks a defender of the d6 square, which is where he wants to park his knight, and that's a good square for the knight because, hey, look, a knight on the 6th rank, and hey, look how close the black king is!'
But I'm not that talented a player, so I'm open to being convinced that I'm wrong. So, tell me why I'm wrong. Tell me why explaining 20.Bg5 in the Petrosian game as suddenly highlighting dark-square weakness is a better, or more correct, or whatever, explanation than the more elaborate one I gave. Or, if you agree with me on that part, tell me why 'dark-square weakness' is a good shorthand.