A semi-tethered jailbreak is one where the device is able to start up on its own, but it will no longer have a patched kernel, and therefore will not be able to run modified code. It will, however, still be usable for normal functions, just like stock iOS, unlike a tethered jailbreak, which would not boot at all. To start with a patched kernel, the user must start the device with the help of the jailbreak tool.
Many of the jailbreaks that use the limera1n Exploit on the iPhone 4 on iOS 7, such as Geeksn0w, included a semi-tethered option. The checkra1n jailbreak only uses a semi-tethered approach.