Controling the center, what exactly does it mean?

I often hear this "controlling the center". Maybe a stupid newbie question but I guess it means that I should try to have more pieces than my opponent (or at least the same) aiming at each one of these four squares so that I would go + after an exchange? 

Does it also mean that I should try to put pieces there in the center? I understand that if I have a safe piece (or a pawn) on one of the squares I do have control of that square, but is it a goal by itself to also have more pieces in the center squares than my opponent or should the main aim be to have "control"?

And when we say controlling the center, are we only talking about the four central squares or does it also apply (but maybe in a lesser degree) to the surrounding squares?

Hi Jocke, I'm a total newbie and just sharing my thoughts. I think the idea is that the opponent should not be able to place pieces on/around the centre without entering a losing exchange. That's why its so good to control with pawns, because almost any exchange will lose material for the opponent.  Having said that, if those squares are guarded by a piece not at the centre- like a bishop on the long diagonal, that's also controlling the centre - just without physically occupying it. So in summary, I think the point is control and not necessarily occupation-  this is the basis of a few openings ( the Reti opening that I frequently encounter is one such).

And yes, the central 4 squares are the most important, but the ones immediately around them are only slightly less important.

My definition is this:  Being able to put pieces on the 4 center squares, also to a lesser extent the other 12 squares that make up the 16 total central squares, without coming out on the losing end after trades. U can physically maintain a presence there. 

Why is the center considered valuable? View  a chess board like a hill with the center the peak and the edges the lowest parts. The center is the more important part from a battle perspective. Imagine trying to fight up hill as opposed to defending from up high. After all, chess IS a war game. Ur pieces can move to more squares the closer to the center they are and it's the number of squares a piece is able to move to that gives it value or strength. That's why a queen is worth more than a bishop, etc. Test this out on an empty board, you'll notice the squares decrease as the pieces move closer the the edges, with the corners being least valuable. 

#1
The center are the 4 squares d4 e4 d5 e5.
Controlling the center means either occupying or controlling from a distance.
Example:
1 e4 controls e4 and d5
1...e5 controls e5 and d4
2 Nf3 controls d4 and e5
2...Nc6 controls d4 and e5
3 Bc4 controls d5
3...Nf6 controls d5 and e4
4 d3 controls e4
4...Bc5 controls d4

So if you value this principle (center control) as very important I guess in practice would mean that you put your knights on c3 and f3?  And if center control is that important, what could be a "valid" reason for not wanting to put your nights on those squares? 

Ur knights will be more valuable in the center (on average, there r always exceptions), but from c3 and f3 they do influence the center and that's a big step towards controlling those squares.

Capturing/recapturing material on another square, needing to support one of your two centre pawns with a pawn, knight might generally not have good prospects on c3/f3 for whatever reason, blocking a check - it’s not that unusual to deploy the knights elsewhere, but also if you’re quite new to chess there’s not much wrong with developing in a basic fashion until you have a good grasp on when the exceptions occur. 

Think of the 4 center squares: d4-e4-d5-e5 as the "high ground".  From there you can see the entire battlefield.  This is what a former coach taught me on how to determine who has more center control.

Keep in mind that is is just a basic explanation:

Occupying any of the center squares with a pawn is worth 2 points of center control. 

Controlling a center square with a pawn is worth 1 point of center control. 

#5
"So if you value this principle (center control) as very important I guess in practice would mean that you put your nights on c3 and f3?  And if center control is that important, what could be a "valid" reason for not wanting to put your nights on those squares? "
Yes, that is correct: f3 and c3 are the natural squares for the knights. So knights are usually developed to those squares. However, sometimes it is necessary to control central square d4 with c3 or central square e4 with f3. In those cases the knights must develop to less optimal squares d2 or e2, or even a3 or h3. From d2 the knight still conrols central square e4. From a3 the knight usually goes to c2, controlling central square d4.
Example:

1 e4 e5 2 Nf3 Nc6 3 Bc4 Nf6 4 d3 Bc5. White can now play Nc3, but also c3 and Nd2.

Another example
1 g3 d5 2 Bg2. The bishop at g2 now controls 2 central squares e4 and d5.

#8
That is a good example, but at first sight black is doing poorly. In reality however, black has traded a wing pawn c7 for a central pawn d4, so black has one more central pawn and black can later even in the endgame play d5 with great central effect.

Putting pieces (meaning non-pawns) in the center is nice when you can do it, but with so many pieces on the back rank, it's usually a waste of time in the opening to do something like bring a knight to a center square. In the opening it's more about claiming territory.

First, it's useful to notice that the less value a piece has, the more it can chase other pieces away. If a bishop and a queen attack each other, then it's the queen that runs away, not the bishop.

Since the pawn has the least value, it is the best at keeping other pieces out of squares. Second best is minor pieces (bishops and knights). Controlling a center square basically means your opponent can't put pieces (and sometimes can't even put pawns) on that square.

And in many openings it's equally divided with each player controlling 2 squares. Let's look at two very basic examples.

In the position below white claimed the dark squares (d4 and e5) and black the light squares (e4 and d5).

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In this sort of structure the c pawn for either player will either support the center (moving 1 square ahead) or try to undermine the opponent's center (moving two squares ahead).

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In the position below we have the same thing but for an 1.e4 e5 opening.

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A useful thing to note about the position above is it's often risky to treat this like a mirror version of the first position by playing moves like f3 or f4. It's risky because that exposes the king. So typically in 1.e4 e5 opening players use the d pawn instead. In fact, usually white tries to save time by playing d2-d4 directly instead of pawn to d3 (as shown above) because now it will cost another move to play it to d4 later.

And black, in many 1.e4 e5 openings, often equalizes the position if they can play d5 without much suffering.

I don't mind a point system like that, because pieces in the center are useful... but I sort of dislike the term "control" ... because whenever a piece moves to a square (any time during the game) that player weakens their control over that square.

For example

Its just what was taught to me by IM Valeri Lilov.  And until im exposed to something better ill stick with it.  And as I stated llama, control and occupy are strictly with pawns. 

That point count idea is an interesting one. It reminds me of a book I studied long ago called Point Count Chess. That might've been by Irving Chervev, not sure. 

It also reminds me of Yasser Seirawans idea of counting the # of squares the pieces target in the opponents half of the board. I love the way Yasser explains things in such a simplified way. 

Sure, like I said it's a useful way to count, and keeping the terminology simple is good for students.

... I just remember once I was analyzing with a 1300 guy, and he played Ne5 saying "I like this because it increases my control of e5" and when I said "it actually does the opposite" he seemed really confused even though IMO it's pretty obvious.

From one of the best chess teachers ever. Yasser explains the center in a very easy to understand way.

#15
Ne5 is sometimes a good move.
Example:

https://www.chessgames.com/perl/chessgame?gid=1058000 

"Ne5 is sometimes a good move"

I don't know how to respond to that.

Easy...Ne5 has nothing to do with what the OP is asking.