When you are setting up internet access at home, you are always concerned about your kid's internet surfing. Kids will be kids and they are curious. If they see something that catches their attention, they are very likely to click on that image or link. If you are not supervising them when using devices, they could possibly end up watching some videos that they should not be watching or accessing a website that they should not be watching. Let's be practical. There are always going to be moments when you are not able to keep an eye on every single click or every single page they are viewing.
So what do we do. You install Antivirus Software or some software that will block access to malware etc. It works as long as your kids do not temper with the installations. To create a safer environment, you can look at updating your home router's settings to use DNS service like OpenDNS. This will ensure that protection is enabled at the network boundary as well. This video talks about risks your kids face on the wild internet highway and what you can do to add safety to their travel.