For starters, you can now create multiple profiles for your kids with your own Google account functioning as the administrator. Forget about teaching your youngsters to share, and set each of them up with their own account.
The new redesign adds some increased functionality to the app's setup process as well, making it easier for parents to deem what content is appropriate for their child.
During setup, you can choose to turn kids' ability to search off, which limits the selection of available videos to the ones shown on the home screen, or recommended by the app. You can set a passcode to keep precocious viewers from modifying the particular settings you've enabled (or disabled).
YouTube Kids does reiterate that your children might stumble upon a video you might consider age-inappropriate, so you do need to keep an eye on what they're watching. You can, however, choose to block videos or channels from ever resurfacing in the app.
Other feature changes make it easier for kids to see videos they can actually understand. Younger viewers will see less text in their interface, while older users will see more text to help them navigate, as well as a wider selection of content to choose from.
The redesign should be rolling out today.