what is a “SHSH”?

The SHSH Blob is an encrypted signature issued by Apple every time iTunes installs or upgrades the iOS firmware on any iOS compatible device (iPad, iPhone, iPod Touch).  In other words, when you upgrade the iPhone’s iOS software, it will first connect to Apple’s servers and ask for permission to carry out the procedure.  Permission is granted in the form of a valid SHSH signature response.
The SHSH signature “system” is designed to give Apple a means to “end of life” or discontinue older versions of the iOS software.  For example (ignore these version numbers), Apple might release iOS 5.0 with a critical security problem that enables a Jail Break.  By ceasing to issue SHSH signatures for iOS 5.0, they can force the iOS user base to skip over 5.0 for a bug fixed iOS 5.0.1.
Apple will only issue SHSH signatures for a limited period of time after new versions of iOS are released, which is why you often times will read: “Save your SHSH’s, iOS 4.x is out!”. Saving the SSH blob is not something that is supported from within iTunes, so it is necessary to use a third party utility called ‘TinyUmbrella’.  ‘TinyUmbrella’ will allow you to forever be able to downgrade your phone to that version associated with the signature.
‘TinyUmbrella’ will play back the saved SHSH signature’s for iTunes, allowing legacy installation of discontinued versions of iOS.  ‘TinyUmbrella’ accomplishes this by intercepting the communication between iTunes and Apple’s servers and forging the signature response back to iTunes.
There are other methods to deal with SHSH saving and playback.  The first method on the scene was developed by Saurik, author of the Jail Breaker’s de facto “App Store”, Cydia. Saurik added functionality to Cydia which allows for automatic saving of SHSH signatures for use later on with iTunes.  Saurik’s method does not require a piece of software to run on your computer, it instead relies a “hosts” file trick which tells an operating system to direct traffic destined for a hostname to an ip address of your choice. In this case, your traffic is heading for Saurik’s specially crafted server which acts the same as an Apple signature server, but will respond with previously saved SHSH signatures when iTunes asks for them.