Whether you want to jailbreak, un-jailbreak, update from an expired beta, or simply update when nothing else is working, putting you iPhone or iPad into DFU (Device Firmware Update) mode can be your last, best hope for success.
DFU mode, as opposed to Recovery Mode, requires a bit of timing and can take practice to get right, so if at first you don't succeed, don't be afraid to try and try again.
At this point iTunes will show you an alert saying it's detected your iPhone, iPod touch, or iPad and it needs to be restored.
If you're curious as to the difference between DFU mode and and Recovery Mode, Ally Kazmucha explains it this way:
Recovery mode will implement iBoot (basically a portion of the bootloader than runs an integrity check) which will not allow you to downgrade your device. DFU mode will still talk to iTunes but it bypasses iBoot which will then allow you to downgrade firmware.
If you're having trouble and need any extra help, check out our Jailbreak Forum.