Jailbreak exploit is actually a vulnerability found in hardware or software of the iPhone or iPad devices. The jailbreak developers use the vulnerability, AKA the exploit to creep through and get into the iOS in order to jailbreak
An exploit takes advantage of a weakness of an operating system, application or any other software code. So if Apple found such, what they do originally is patching it with a software update. (If the vulnerability is a software exploit. )
Among many exploits, zero day exploit is the concerned exploit in jailbreak community.
Zero day exploit is an exploit which takes advantage of a zero-day vulnerability. A zero-day vulnerability occurs when an operating system contains a critical security vulnerability of which Apple is unaware.
The vulnerability only becomes known when a hacker is detected exploiting the vulnerability.
Once such an exploit occurs, iOS is left vulnerable to an attack until Apple releases a software patch to correct the vulnerability and the patch is applied to the iOS.
So this is the basic introduction of a jailbreak exploit. There are many jailbreak vulnerabilities or exploits available in the jailbreak community. Most of them were patched by Apple and some of those were released as jailbreaks.
Now the latest iOS 13 jailbreak and higher are also under the spell of checkm8 jailbreak exploit which was found by famous hacker axi0mX. Checkm8 jailbreak is a hardware expolit and now turned into Checkra1n Jailbreak(For macOS) and ra1nstorm jailbreak (for Windows and Linux) tools.
Then, there were many exploits fornd for iOS 12 as Dany Lisiansky who is a hacker was able to find another exploit for iOS 12.2 but unc0ver and chimera were the only publicly available jailbreak tools at that time for iOS 12.2. Read here for more details on iOS 12 - iOS 12.4.6 jailbreak.
Keen jailbreak performed a zero day vulnerability at MOSEC which happened in 2017. But this was not released as a public
Then in iOS 11, Ian Beer was able to find a few exploits under project Zero. Even Keen labs also found an exploit, but they revealed this exploit to Apple’s bounty program.
In iOS 11.2.6, Alibaba engineer Min Zheng found a zero day bug. Even in iOS 11.3, Ian Beer and SorryMyBad found exploits.
In iOS 11.4, Jailbreak was achieved by Electra Jailbreak, Min Zheng was able to find two exploits but they were reported to Apple and were patched. Tihmstar’s v1ntex exploit for 4K devices running iOS 11.4.x also made a huge talk back in 2018s.
Then again at MOSEC 2018 team Vulcan was able to demo a remote jailbreak with an exploit. But was never released as a public jailbreak. Before Unc0ver and Chimera were found for iOS 12, there were some sandbox escape releases but those were never implemented upto public jailbreaks.