A semi-untethered jailbreak is similar to an untethered jailbreak, but it gives the ability to start the device on it's own. On first boot, the device will not be running a patched kernel. However, rather than having to run a tool from a computer to apply the kernel patches, like a tethered or semi-tethered jailbreak, the user is able to re-jailbreak their device with the help of an app (usually sideloaded using Cydia Impactor) running on their device. In the case of the iOS 9.2-9.3.3 jailbreak, a Safari-based exploit was available, thereby meaning a website could be used to rejailbreak.
Some semi-untethered jailbreaks can be completed entirely on the device using a sideloaded app (which still requires a computer). Others require a computer to be used first, and then an app or website can be used to rejailbreak after each reboot.