Of all the content providers YouTube is probably the one you want to keep your eye on if you don't want your kids watching inappropriate content. Since most of it is user generated you can find anything from explicit material to just viral stupidity kids will try to recreate.
If you have children that you don't want watching mature content on your iPhone, iPad, Mac or Apple TV, you'll have to block it on each individual provider - there is no catchall setting that does the trick. That means you have to go into Netflix, Amazon Prime Video, Hulu, YouTube, HBO and any other content provider you might have a subscription to and set up restrictions in one form or another.
As of yet there is no universal way to block your children from watching unsuitable content at the device level - so you can't just go into your Apple TV settings and block all rated R movies, you have to go into each content provider's settings to do it. If you have Amazon Prime Video, you'll have to go into its settings to restrict viewing, same for Netflix, Hulu, Apple TV+ HBO and so on. Here's how to restrict viewing on Netflix:
The U.S. and many other countries have rating systems for video and audio media to let parents know if the material is explicit or otherwise suitable/unsuitable for their children based on age. If your child uses your iPhone/iPad/Apple TV/Mac and you are concerned with what content they may be viewing, you probably want to restrict it somehow. This can be a headache considering how many sources there are.
Apple Arcade is Apple's video game service that launched in the fall. A five dollar monthly subscription gets you access to tons of games, which can be quite addictive for youngsters and adults alike as we've seen with the recent Fortnite craze. If you don't want your kid playing games all day long or playing with other people online or making inn-app purchases, Screen Time will let you set these restrictions.