Firmware downgrading

Downgrading is the process of restoring to an older firmware. Apple does not allow downgrading unless the firmware is being signed. Downgrading is only possible on A4 or older devices that have bootrom exploits such as Limera1n with the exception of iPhone 4s that can be restored from 5.x to 5.x as long as there are valid SHSH blobs saved for both the iOS the device is on and the one the user wants to get. It is also possible to downgrade an iPad 2 to 5.x with 4.x and 5.x SHSH or 4.x with only 4.x SHSH blobs. iPhone 4s and iPad 2 downgrading will require redsn0w.

Reason for downgrading
Some users downgrade since iOS 7 does not run as people want on older devices like the iPhone 4. This can also be for nostalgia. There's many reasons to why one would want an older iOS.

Restoring to Older Firmwares via Any Method
Downgrade iTunes to 11.0 or 10.7 and then restore when in PwnDFU.