What is the strategic significance of the English Opening? I enjoy playing the English opening, pushing my pawn to c4, and trying to out flank my opponent.  But I have a hard time, outside of playing normal lines, understanding the advantage it gives, and why it leads to fantastic games.  Any insights?
Since I was playing the English myself, I can tell you why I have found it a good opening for me:


Transpositional potential of this opening is stunning! You can lead your opponent out of his/her opening and draw them into the variations they do not know. One small example: 1.c4 c6 Since Black reveals to us that he plans to play Slav/Semi-Slav/Queen's Gambit we can steer the game into Caro-Kann with 2.e4!?. Now, this means nothing objectively--we just left one opening to enter into another--but the psychological effect can be devastating! It can lead to such consequences like deflating their will to play the game since the game is "boring", or you can actually transpose into an opening your opponent does not know and quickly demolish him.
The center remains fluid for a long time. This is truly gold in the hands of the experienced player and answers this part of your question: 



  why it leads to fantastic games?


You see, since White restrains himself in the center, it is usually safe to play on the wings. Black usually responds by playing on the wings too, but inexperienced players forget about counter attack in the center. This possibility requires good calculation and accurate evaluation of the current position in order for a player to be able to execute this properly. Action on one wing + counter-attack in the center = crazy game. Launch your counter-attack in the center at the proper moment and you will win the game most of the time.

These are the beauties of this opening:


Its intolerance for "robotic play" and opening memorization--it requires of a player true knowledge. You must know how to play chess--opening, middle game and end game--no opening book can save you if you do not know how to play chess.
Its main feature is to give so much space to a "true" player for creating winning chances. If you are creative enough you can win in the opening, middle game and even an endgame. By "true" player I mean player who plays every game with 100% of his strength. The player who plays with knowledge and does not rely on safe patterns/30+ memorized opening moves and so on. The player who is willing to fight for victory to the very end.


Whether you play "normal" lines, or you play some side-line/transposition, the English opening will never be dull and sterile for a player who is prepared to invest all of his mental capacity to win the game.

Hopefully this answer will help you.

If you have further questions leave a comment.

Best regards.