The significance of center control gives you an advantage in space. To elaborate, space is the territory in which your pieces are safely allowed to advance in, and also a territory that is unsafe for your opponent to move to.
This is an ideal center since every minor is activated, and guarding spaces, making it difficult for the opponent to advance, and compressing the opponent's pieces.
Space
A more in-depth look into space and attack. To reiterate, space is the "control of squares". When acquiring space, you ought to consider where exactly are you attacking, "Plan of development" you develop your pieces towards where you are planning on attacking, preferably where the enemy is vulnerable, More often than not this would be the less developed area.
Your space should compliment your pieces' ability, giving you a better position. Understand that your position influences how your pieces perform. Certain Positions give pieces more value and more control over spaces. Other times pieces are hindered by bad positioning, making them inactive or less valuable.
Active Pieces
Activating your pieces is an important part of developing. Especially at high-level games utilizing your entire arsenal gives you a distinct advantage against someone who doesn't.
The activeness of the piece depends on the square it occupies, the squares it controls, and the pawn structure around it.
An inactive piece is pieces that are unable to move to any square or very few squares.
An active piece is defined by a piece that is capable of moving to a large number of squares or the maximum amount of squares of its type.
In other words, activity has a lot to do with mobility. Furthermore, the activity of pieces in defense is important to understand.
When looking at defenses there are generally two types: Active and passive defensive moves.
Active defense moves involve using you use your pieces to actively threaten other pieces instead of only defending your threatened pieces. By doing this you hinder your opponent's developed attack, and you are given the opportunity to counter-attack.
However, there are many situations where you are not given the opportunity, in that case, you are forced to passively defend your threatened pieces, and making no threats yourself.
Pawn Structure
As mentioned before your position is improved with well-placed pawns. Pawns are the soul of the game, they may seem expendable but are crucial for a well-developed position, and especially important for an endgame.
Not One Step Back
Pawns cannot move backward, so every move should be evaluated before executing, you want to make sure that the move you commit is an effective and secure one.
The strength of the Pawn structure is determined by the amount of "Pawn Weaknesses" are present throughout the structure.
Pawn structures offer great insight into openings, generally, you should be attacking in the general direction of your pawn chain, without properly developing your pawn structure you have no clear direction for an attack.
Pawn Strengths:
Passed Pawns
Connected Pawns
Pawn majorities
Pawn Weaknesses
Backward Pawns
Doubled pawns
Hanging Pawns
Isolated Pawns
If a Pawn weakness is spotted, it makes way for important breakthroughs, such as opening up diagonals and files for your bishops and rooks to exploit.
Bare Bones Breakdown of Positioning
Control Of Center
Space Control
Active pieces
Observing Pawn Structures
Center Control
The significance of center control gives you an advantage in space. To elaborate, space is the territory in which your pieces are safely allowed to advance in, and also a territory that is unsafe for your opponent to move to.