The central pawns are most important. They establish the control of center with the smallest means possible. The hyper-modern chess theorists ( say after Nimzowitsch) of the 1940’ s and 1950’s in some cases advocated less importance on them. As the game wages on the pawns on the wings grow in strength, but in the opening and middle game they are very important.
You do not want many pawn islands or backward pawns or isolated pawns, these can deteriorate your position and cause a lost game.
Sometimes you can create what is called a “poison pawn”, which is a tactic of offering material in exchange of positional advantage. It can be accepted or declined. In many cases its a pitfall to take the pawn if the other player knows how to capitalize on his new position.
If you lose your pawns in the center you over burden your other pieces and this can cause you to lose a better piece.
Also, never move your pawns that protect your castled king. in the endgame, your king grows in importance and will take the stage and move to the center and attempt to get a passed pawn.
Also the central pawns can anchor your other pieces ( knight and Bishop) and protect them too.
Lastly, you usually want to capture toward the center of the board to stabilize your control over the central squares.