Jailbreaking allows you to get your hands dirty with your iPhone in ways that Apple does not appreciate. This is a reason why, post every major iOS release the jailbreak community has to work round the clock to find new loopholes in the security systems in order to bring jailbreak to the devices as Apple shuts down the previous vulnerabilities, inevitably.
There was no news about the jailbreak of iOS 7.1.1. Until now. The untethered jailbreak has been finally made available for iOS 7.1.1 by a group of Chinese developers called Pangu. Pangu have released the software that claims to be able to install Cydia on your iPhone/iPad/iPod Touch running iOS 7.1 and above. You will need to download the .exe file from the website linked below for your Windows PC and install it. You need to have the latest version of iTunes installed on your PC for the process to go through, so make sure you have that checked. Connect your iPhone to the computer and go ahead and jailbreak the device while following the onscreen instructions.
For those on Mac, the wait for a jailbreak will continue as the Mac version of the tool is very much in works and not ready for a release just yet. The only reason why we are unsure of going ahead with the process is because the exe file seems to be suspiciously large at almost 70 MB. So far, most of the jailbreak softwares have not been anything more than 30 MB or so. However, so far there have been no reported cases of any sort of malware or spyware and the size of the file appears to be fairly non risky.
However, with the exploit out now, it would not be beyond the realms of imagination to see some of the more famed groups like evad3rs to come out with a more reliable jailbreak. However, if you are feeling adventurous and have a spare iDevice that is running iOS 7.1 or above, you can go ahead and give this a try. Of course, if you do that, make sure to drop a word on your experience.