Something tutorials never seem to teach

Still being a novice, I sometimes find tutorials and books about how to improve.  One thing I've noticed is that a great many tutorials and videos and such mention "I'm eyeing the c5 square" or "you notice he's left the critical f6 square" and the like.  The problem is, I've never heard anyone explain why certain squares are so important during different games.  Why, in some games, does it seem like both players are struggling over and empty square as if they both know that square is critical to something?

How do you recognize these squares?  What makes them "critical"?  Outside of the obvious 4 center squares, of course.

Should explain pretty much everything for you:

https://www.chess.com/blog/Cherub_Enjel/1-how-to-understand-everything-in-a-chess-game

The reason that certain squares are important is that:

(1) You want to checkmate your opponent

(2) Your opponent will protect the king with his/her pieces

(3) So you have to destroy those pieces

(4) But your opponent won't just let you win those pieces, if he/she is somewhat competent

(5) So you have to put pressure on the opponent's targets - weak pawns are obvious targets, because winning a pawn can get you a queen (promotion), giving you the force you need to do (3) and (1). 

(6) taking control of certain squares means you can put certain pieces on those squares, to increase their activity, which targets weak pawns and restricts the opponent's pieces, and this lets you do all the above. You can also attack the opponents king in some cases, and force him/her to sacrifice pieces/pawns to protect the king, and win that way too.

So really, the idea is that you'd love to do Scholar's mate, but it's not reasonable. So you try in different ways that don't compromise your position so much. 

 Quite an informative post, I enjoyed it.  That answers my question quite nicely -- now the hard part is focusing enough to see these squares.

Yeah - training is improving your skills and learning to apply stuff in practice, which is the part that makes chess really difficult.

I first started paying attention to critical and weakened squares when I realized how much it sucks for your opponent to have a pawn protected, unopposed knight post up within checking distance while also covering a lot of other squares restricting my movement. Preventing that or looking for my own advantages, helped me getting started on squares. Squares are so important. 

Quite a complex topic really.  Always going to depend on the position......Something like this the d5 square is vital because the d6 pawn is backwards and weak(assuming there are a lot more pieces on the board.  Just left only the knights there to simplify it for you).  If black can play d5 in these types of situations without tactical consequences he will have at least an equal game in general.  Getting rid of the weak d pawn and activating his pieces.  So this is why white will play bg5 and exchange off the defending knight to be able to land on d5 (or just control the square) or create more pressure on the pawn while the d pawn is immobilized.  The exchange of light squared bishops in this position would greatly benefit white in general as well.  Then the square becomes even more weak.

It did? I've only scanned the Wiki page but so far have only seen it called "a decisive naval battle" and "a turning point in the Pacific war". Nothing quite as superlative as you say, though.

Let's be honest, if it weren't for the Russians on the Eastern Front, WII could have gone a bit differently. According to Wiki: "The Eastern Front was decisive in determining the outcome of the European portion of World War II, eventually serving as the main reason for the defeat of Nazi Germany."

If it's a strategic idea, mostly by experience. A player often has a reference game or arrangement of pieces in mind when they say such a thing. So having to be told isn't so bad, because now you're getting experience. You're being offered a reference position.

 You're not necessarily expected to understand right away. Even if it doesn't make sense, keep watching or reading and see if it doesn't make sense as you see the game unfold. Sometimes it's not an abstract strategic idea, sometimes it's a concrete tactical idea. Like the only way to defend a mating pattern is to defend with a knight on f3. And the only way the knight can get to f3 is through d4. So they might say "d4 is critical"

When it's a strategic idea, it's often something like already described by others above. In particular remember when an empty square is occupied by a piece, that piece attacks many squares around itself. So in a sense the square itself isn't so important, it's that, once a piece lands there, it may be close to the enemy king, weak pawns, loose pieces, things like that.

Well said, The_Chin_of_Quinn