Children hide what they have been doing from other people for the same reasons anyone does.
(1) Kids hide things from their parents because they feel it is "theirs" in some way. It's personal or intimate, or they're not sure how they feel about it yet and just don't want to share. They might feel that sharing it with an adult - who will invariably have an opinion or vested interest - will "wreck" that part of it.
(2) Some things are hidden because the kids don't think the parents will understand. Think of how you might "manage" your older parents: there are some things they just don't understand about how the world is in your context that was different from theirs. Kids, particularly teens, will do this.
(3) Finally some things are hidden because the child is ashamed. They know they did something wrong, made a poor choice, made a mistake.
So as a parent, there are three things you can do to encourage sharing these stories:
(1) Let them define their boundaries. Really if they don't want to tell you, it's none of your business. Allow them to have an internal life that is separate from you. If you're anxious or tense and that's why you want to know about everything that happens to them, then try to keep in mind that requiring children to have no privacy so that you as the adult can feel less anxious is really not terribly fair. You need to deal with your anxiety in a different way.
(2) Do your best to ask your child to explain to you the differences between their world and yours, acknowledge the difference and then DON'T JUDGE! Above all, don't say your way was better. You can talk about irrelevant parts of school for example: "When you all eat lunch, do you eat quickly and then go play? Or do you just hang out and talk? ... we didn't have cell phones / game boys / computers at school when I was a kid!" So you're really just discussing the new world and learning about it for no reason other than you're genuinely interested in how things are done nowadays. This will come in handy when your child is an adult and they've got their hands in cool stuff!
(3) This last is the toughest one. In order to minimize the ill effects of shame, we have to be very good at "picking our battles." Every parent draws lines differently here, but I urge you to try to avoid shaming children unless what they've done is truly shameful.
All people make mistakes. We need to learn how to transcend them, and it's difficult to gear up to fix a mistake while feeling ashamed. We also need to avoid making the same mistake repeatedly. Since we don't imagine emotions well and we can't remember negative physiological effects, shaming people isn't as effective as one might hope. The real threat of shame is the threat of isolation, of the child imagining the parent genuinely rejecting them, at least temporarily. Please use this rarely.
If you can keep a home environment where you don't constantly ask them questions about what is going on, where you are genuinely interested in learning about their life context, and where you can help them through their mistakes, your kids will be more likely to confide in you.
They still may not! They may still just want privacy! But they are more likely to do so.