Back when the original iPhone was released in 2007, iOS users have been trying to jailbreak their devices already. Basically, jailbreaking an iOS device entails the use of hardware and software exploits to gain root access and remove limitations that Apple set. In a jailbroken device, users can install unauthorised applications, themes and tweaks that are not available in the App Store.
A number of popular iOS features started in the jailbreak community and were just added by Apple into the native iOS features eventually. A good example is the iOS 7 Control Centre and the multitasking ability, which started as tweak developers created for jailbroken devices.
The iOS 7 was released on September 2013 and its first jailbreak was released on December 2013 by the Evad3rs team using an exploit found in iOS 7. However, with the release of the iOS 7.1, the exploit used was patched by Apple and even publicly thanked the Evad3rs team for finding those security bugs. As such, it was believed that an iOS 7.1 jailbreak will be quite tricky to achieve. On the other hand, it might not be the case anymore as a video showing a jailbroken iPhone 4 running on iOS 7.1 was released online.
A video was posted on YouTube by the jailbreaker Winocm, proving that the iOS 7.1 can be jailbroken. Although this is great news for iOS 7.1 users who are waiting for the jailbreak to come, there is a huge catch - the jailbreak only works for iPhone 4 and its A4 processor. Basically, devices with A5, A6 and A7 processors cannot have the iOS 7.1 jailbreak just yet.
Although the current jailbreak only works with the iPhone 4, this might indicate that devices with A5, A6 and A7 might see a jailbreak solution for their devices in the future as well.
Meanwhile, if you have those devices and already jailbroken, you might want to steer clear from the iOS 7.1 update and wait for a jailbreak to be released for your device.