[angrymcdouble]

If your iPhone-iPad-iPod is on 8.4 and jailbroken (if not follow this thread), don't restore it, it will update to iOS 8.4.1, it is not jail breakable at the moment, use this method instead!

Cydia Impactor (by Jay Freeman (@saurik)) allows you to restore your jailbroken device to its original state (no jailbreak, no data, no update of the firmware) and it can repair/reinstall damaged/lost system files. The best thing: everything is done on your device.

Semi-Restore (computer) and iLex Rat (on the device) were two alternatives, but they didn't remove the jailbreak. They are also not compatible with iOS 8.3-8.4 yet.

Compatible with:

Devices:
iPhone 4S - iPhone 5 - iPhone 5C - iPhone 6 - iPhone 6+
iPod Touch 5G (NOT THE 6G)
iPad 2 - iPad 3 - iPad 4 - iPad Air - iPad Mini - iPad Mini 2

iOS:
iOS 8.3 - iOS 8.4

Why is it useful ?

Some quick examples:
-The last iOS version isn't jail breakable anymore, and you wish to start fresh on a newly jailbroken device. Cydia Impactor will allow you to do this, as it won't go to the last firmware available, it will use the current firmware.

-You want a quick and easy way to remove a jailbreak (before a warranty return or a sale)

Before

1/ Make a backup of your data (if it's important to you), because everything will be erased.

2/ Make sure you know the iCloud account (email and password) if Find My iPhone is enabled, you'll need it to unlock the device. If Find My iPhone is turned off in the settings, it won't ask for it.

3/ Preferably connect your device to a power source, or make sure the battery is charged more than 20%.

Tutorial

1/ Open Cydia

2/ Search for "Cydia Impactor"

3/ Tap "Install" in the top-right corner and "Confirm" after.

4/ "Impactor" app will be on your Springboard, start it.

5/ Tap on "delete all data and unjailbreak device"

6/ You're all done, in a matter of minutes you'll have a new device, in an unjailbroken state, without the need of any computer

FAQ:

How does this work ?:
Saurik was kind enough to provide some technical details:
Spoiler (Click to View)

Impactor uses the firmware archives provided by Apple for its "over the air" update feature. These files are ~2GB large, so Impactor goes to extreme lengths to minimize the amount of data it needs to download: most recoveries will require less than 10MB of transfer.

First, the update's "bill of materials" is compared against the files on your device, generating a list of changes.

Then, all files on your device that have been modified or otherwise destroyed are downloaded directly from Apple.

In a series of carefully calculated file migrations, all new files are moved to the user partition, and all system data is moved back to the system partition.

Up until this point, the idea is that no changes to your system have been made that are "unsafe": at any point, if Impactor fails/crashes or your device reboots, you can just run it again later.

Finally, all of the staged changes to the filesystem are "committed", all user data is deleted, and iOS is told to run its "reset all content and settings".

The idea is that this "critical window" lasts only the final few seconds of a process that lasts for multiple minutes.

(That said, I still highly recommend not at all "messing with" the app while it is running, and maybe if you have a lot of data this will take longer than I expect.)

When the device reboots, it will look as it did when you first turned it on; it will also no longer be "jailbroken": if you want to jailbreak it, you will need to do so using a desktop jailbreaking tool.

Can I jailbreak after?:
Yes, you can totally jailbreak after. Consider your device as a freshly restored one.

[Sennheiser]

why not just dfu mode the device and restore it?

it is safer to do that lel

[Λlex]

why not just dfu mode the device and restore it?

it is safer to do that lel

Did you not read the entire thread? Updating/Restoring your device through iTunes will prompt an update to the latest firmware. Cydia Impactor won't. And besides, Cydia Impactor is faster than iTunes, since iTunes needs to download the firmware before you can restore the iPhone.

[angrymcdouble]

^
No problem !
-characteeeers-

[CyanogenMod]

Awesome guide, knew about this before hand (Works great as I just reverted back to clean 8.4 4 hours ago with this) but many members will use this seeing as 8.4.1 has been pushed to public today.

[angrymcdouble]

Most of the people will restore to 8.4.1 and while looking for a downgrade, they will find this x)