Different devices and versions are exploited with a variety of tools.
A jailbroken device permits root access within the operating system and provides the right to install software unavailable through the App Store. Typically it is done through a series of kernel patches. On Apple devices running iOS and iOS-based operating systems, jailbreaking is the use of a privilege escalation exploit to remove software restrictions imposed by the manufacturer.
Not to be confused with bootloader unlocking or SIM unlocking.