evasi0n is, as expected, a solution of jailbreak downloaded by millions of iDevice owners who waited almost 6 months for its release. Although it took so much time for its development, the solution is extremely complex and was built avoiding the security measures imposed by Apple in iOS, the name being extremely well chosen. Instead of removing everything that Apple thought to prevent a jailbreak, hackers have found ways to avoid all those obstacles and so now we can all jailbreak iDevices.
Evasi0n begins by running libimobiledevice, a program that substitutes for iTunes to communicate with iOS devices via the same protocol as Apple's program. Using that tool, Evasi0n exploits a bug in iOS's mobile backup system to gain access to certain settings that it normally shouldn't be able to access, namely a file that indicates the device's time zone.
A Forbes article, planetbeing talks about how the jailbreak solution was developed, in a another article you have explained everything with a bit more details about the execution, but I recommend you to read them only if you are really interested and have worked with iOS before.
