user12834: 
Why is pawn to c4 opening advantageous in the screenshot above?

user7002: c4 in general, controls more central square, opens Qa4 diagonal, gains Q side space. Your N can now hop to c3 without blocking your c-pawn (and in turn blocking your Q to a4 or b3).
c4 in this particular position (Queens gambit) is as @DammJoe said. To challenge d5 and black's center and white can easily regain it if black takes immediately.

user12540: The Key Centre Squares of Chess are e4,e5.d4,d5 . Usually any of your Piece resides in these Squares it provides more Centre Control and best possible activity . Now coming to your Q c4 tries to deflect Black's centre pawn and opens up a diagonal for White . You see that White captures back the pawn with a Check and Queen gets activated . Similarly the c-file for White also opens up in this case . 

user12830: Because if black takes on c4 it loses Control of the centre and white will generally get that c pawn back sooner or later

12834: <p><a href="https://i.stack.imgur.com/ee4ym.png" rel="noreferrer"><img src="https://i.stack.imgur.com/ee4ym.png" alt="enter image description here"></a></p>

<p>Why is pawn to c4 opening advantageous in the screenshot above?</p>
 7002: <p>c4 in general, controls more central square, opens Qa4 diagonal, gains Q side space. Your N can now hop to c3 without blocking your c-pawn (and in turn blocking your Q to a4 or b3).</p>

<p>c4 in this particular position (Queens gambit) is as @DammJoe said. To challenge d5 and black's center and white can easily regain it if black takes immediately.</p>
 12540: <p>The Key Centre Squares of Chess are e4,e5.d4,d5 . Usually any of your Piece resides in these Squares it provides more Centre Control and best possible activity . Now coming to your Q c4 tries to deflect Black's centre pawn and opens up a diagonal for White . You see that White captures back the pawn with a Check and Queen gets activated . Similarly the c-file for White also opens up in this case . </p>
 12830: <p>Because if black takes on c4 it loses Control of the centre and white will generally get that c pawn back sooner or later</p>
