Backups, apparently. According to the info provided by services mentioned in the article on how to set up tracking on iOS devices there seem to be two approaches to this:

One service says "In order to monitor device activity like texts (including some deleted ones!), web browsing, notes, and the camera roll on an Apple device, we'll need to perform regular backups to a computer. This is because of Apple's stringent security on their devices, which prevents regular apps from monitoring those activities. After the first-time setup, activities will be backed up wirelessly over Wi-Fi whenever your child and their devices are home."

The second one seems to be using iCloud backups, in the requirements on how to monitor iOS devices it says "Just iCloud ID & Password are required, iCloud backup should be enabled on the device."