To conserve is to save or protect something, like money, or your energy on a long run. People are also encouraged to conserve energy by turning off lights and not cranking the air conditioner.
Conserve is from the Latin for "to keep, preserve, guard" (conservare). Con means "together," so "together" we can "serve" the planet by not doing doughnuts in the wetlands on our jet skis. You can conserve the planet or a little something for yourself — you might conserve hot water so you can wash your hair later, or try to conserve your old bedroom when you go off to college (and your mom is ready for a home office).