If possible, bring a telescope or a pair of binoculars, and have your kids look at the stars and identify constellations and planets. When camping, especially if you can get farther from a city, the night sky is brilliant with stars that your children may never have seen.
Many campgrounds are in places like state and national parks, which offer a wealth of easy to moderate hikes. Try taking your kids on a hike or two. Do not make the hike about achievement only. The goal should not simply be to reach the top of a mountain. For most children, hiking is about exploration. Bring guides to the flora of the region and show them plants such as poison ivy and teach them how to identify it.
If local fire regulations permit it, build a campfire and have your kids cook S'mores over it, or roast hot dogs on a spit. Try cooking corn on the cob in aluminum foil over the campfire. While building the campfire, take the time to show your kids how it is done, and have them help by gathering firewood.
Teach your kids how to set up the tent, and have them help do it by unfolding the tent poles and attaching the clips to one of the poles. Show them how to pound the tent stakes into the ground and give them an opportunity to do so.
If your kids are old enough, try bringing a second tent for them and have them set it up and sleep in it so they can take ownership of the camping experience.