The term "jailbreak" is the process by which some form of arbitrary code execution (usually by spawning of an SSH shell) is obtained by exploiting the kernel (and other protections, such as AMFI, PAC, PPL, KPP, and KTRR - but these do not apply to every software version) of iOS, iPadOS, watchOS, tvOS, audioOS, or bridgeOS. It used to be done by patching /private/etc/fstab to mount the System partition as 'read-write'. This is entirely different from an unlock. Jailbreaking is the first action that must be taken before things like unofficial activation (hacktivation), and unofficial unlocking can be applied.
Older jailbreaks also included modifying the AFC service (used by iTunes to access the filesystem) to give full filesystem access from root. This was later updated to create a new service (AFC2) that allows access to the full filesystem.
Modern jailbreaks now include patching the kernel to get around code signing and other restrictions. These are called Kernel Patches.
Note: The legality of jailbreaking your device varies with each country/region. Wikipedia has a summary of legality for some countries.
Types of Jailbreaks
Tethered : The device must be booted using a computer every time, otherwise it won't boot at all. This type of jailbreak is uncommon. This is because, starting with the iPod touch 2 (new BR) and iPhone 3GS, Apple has signature checks for its bootchain, which includes LLB, iBoot, and the Kernel, meaning a custom bootchain cannot be loaded unless an exploit is used to patch these checks. Example of tethered jailbreaks are 4039, blackra1n, and orangesn0w.
Semi-tethered : The device must be jailbroken using a computer every time it's rebooted, otherwise it will boot in unjailbroken state. Examples of semi-tethered jailbreaks are opensn0w, geeksn0w, checkra1n, or palera1n. They are similar to tethered jailbreaks in how they jailbreak iOS, but they don't modify iOS' default bootchain - instead sending their own custom one.
Untethered : Untethered jailbreaks were originally how almost every jailbreak was - run the jailbreak once, and then you're jailbroken for life. They could be installed via Safari with JailbreakMe, or with a computer, using redsn0w, Absinthe, or Pangu. However, these types of jailbreaks started to die out in iOS 9.
Semi-untethered : Starting with iOS 9, it was no longer easy to make a fully untethered jailbreak, so devs instead created semi-untethered jailbreaks. These jailbreaks are run using an app which jailbreaks the device, but after a reboot, the app will need to be run again - otherwise the device will be unjailbroken. Examples of these are Home Depot, Meridian, unc0ver, Chimera, Taurine, or Dopamine. Due to Apple limitations, the app must be resigned every week (or every year with a paid developer account). Tools like ReProvision Reborn were created to automate this process. Additionally, with iOS versions compatible with TrollStore, it is possible to permanently sign the jailbreak app so it will never expire.
Latest firmware and Jailbreak status
For other devices, firmware versions and jailbreak tools, see the versions list below.
Untethered or semi-untethered jailbreaks are shown with a green 'yes'. Tethered or semi-tethered jailbreaks will be stated in a yellow box. Beta Firmwares are not listed.