SHSH

As the SHSH blob article on Wikipedia summarizes it: "SHSH blob is a jargon term for a small piece of data that is part of Apple's digital signature protocol for iOS restores and updates, designed to control the iOS versions that users can install on their iOS devices (iPhones, iPads, iPod touches, and Apple TVs), generally only allowing the newest iOS version to be installable. "

Technically, the SHSH of a firmware image is a 1024-bit ( bytes) RSA signature. This often also refers to backup files with the signature ("SHSH blobs"). This signature is needed to restore a specific iOS version; it is generated by Apple based on hardware keys of the device and the hash of the firmware. Apple only issues signatures for the currently-available iOS version, which disallows installing older iOS versions. But if you have saved signatures for an older iOS version, you may be able to use a replay attack to restore that version. Therefore it is recommended to save the signature for your device as long as Apple issues it.

With the tools mentioned below it is possible to backup the signature. It is not necessary that the device is jailbroken to do the backup. Usually the SHSH signature file is stored on Saurik's server. If it is stored there, then you can see in the top of Cydia (on jailbroken devices) for which version a backup exists. This moved to TSS Center which can be located on the main page and then they are shown at the top of that.

Users often misunderstand this system and think that the SHSH firmware version they back up depends on the firmware version they have installed on their device. This is the case for iFaith, but not for TinyUmbrella. iFaith dumps the SHSHs from your device's storage (whatever's installed on your device, e.g. 4.3.3), while TinyUmbrella gets SHSHs from Apple's servers (whatever firmwares Apple is currently signing).

Using SHSH
Older devices (iPhone and iPod touch) do not use SHSH signatures, so installation of any firmware on these devices is possible.

iPhone OS 1.x and 2.x do not use SHSH signatures, and can therefore be downgraded to at any time, even on devices that do use SHSH signatures, such as iPhone 3G.

Versions above iPhone OS 3.0 require the iBEC, iBSS, and LLB to be fully signed with an SHSH for the ECID of that device.

However, some devices are vulnerable to untethered bootrom exploits, such as 0x24000 Segment Overflow or alloc8. These devices can be restored to a custom IPSW in Pwned DFU Mode for any version that is available to that particular device. Notable devices vulnerable to untethered bootrom exploits are the iPhone 3GS and iPod touch (2nd generation). The limera1n Exploit is able to provide a tethered downgrade for vulnerable devices.

Since various exploits, such as the limera1n Exploit, are fixed in the bootrom since version Bootrom 838.3 and because iOS versions 5.0 and above includes a nonce in their SHSH hashes, downgrading newer devices is not as simple. Blobs must be stitched into a custom firmware, and restored to in Pwned DFU Mode.

Blobs can be saved with tools such as iFaith and TinyUmbrella. Firmwares can be stitched using iFaith, redsn0w or sn0wbreeze.

Newer methods such as Odysseus, Prometheus or iDeviceReRestore are used now because other tools have become outdated and newer versions of iTunes prevents restores to custom versions.

Timeline
As noted above, the original iPhone and iPod touch didn't use SHSH blobs. iPhone OS 1.x and 2.x didn't use SHSH blobs either.

Protocol
To request a SHSH blob from Apple, a simple HTTP request can be made. For a full description, see the separate articles SHSH Protocol and Baseband SHSH Protocol.