In battle, we are warned that we may not wantonly destroy fruit-bearing trees. This is part of a greater principle called b'al taschis, which means not to casually destroy things that are or may be useful. This includes, for example, smashing utensils in anger or wasting perfectly good food. The Talmud in Shabbos (105b) compares one who smashes things in a fit of rage to an idolator, since he impulsively does whatever his inclination tells him to do.
The reason for this mitzvah is so that we should appreciate the good things God has given us. Yes, burning down an apple orchard, for example, might dishearten an enemy, but we have to look at the big picture. We have to recognize the value of what God has made and not ruin it in our short-sightedness. Similarly, we should not throw out edible food or destroy usable objects, as doing so shows a distinct lack of appreciation for God's gifts.
It should be noted that fruit trees may be cut down for constructive purposes, such as for their lumber or for the overall benefit of an overcrowded grove.
This mitzvah applies to both men and women in all times and places. It is discussed in the Talmud in the tractates of Baba Kama (91b-92a) and Baba Basra (25b-26b). It is codified in the Mishneh Torah in the sixth chapter of Hilchos Melachim. This mitzvah is #57 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #191 of the 194 negative mitzvos that can be observed today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.