Right now, its key feature is an end-to-end exploit of the Android "Master Key" vulnerability, allowing a user to obtain root access on many Android devices (including Glass and TV).
It also exists, separately, as an iOS application available via Cydia Installer. This iOS tool's key feature is to remove and revert all changes made to the device and return it to "stock" Apple iOS software without updating to a new version of iOS.
Download Cydia Impactor for Mac OS X, Windows, Linux (32-bit), or Linux (64-bit). (These URLs will always redirect to the most recent versions, so feel free to directly link to the packages from howto guides.)
If you are on Windows, you may have to install a device driver to talk to your device over USB. If your device is not detected, use Impactor's USB Driver Scan feature to attempt to automatically construct and install a driver for your device. You do not need the Android SDK.
To download new versions, use "Check for Updates..." under the Impactor menu from inside of the application. Impactor will also occasionally prompt about new versions that come out. (This feature is currently not available in the Linux versions.)
If you are having problems using Cydia Impactor (it crashes, doesn't work on your device, or simply doesn't make any sense) please join #android on irc.saurik.com and ask a question.
If that bug is not available, Impactor will instead attempt to use a different signature verification bug. For more information on how that bug works, I have done another article on the new exploit.
It is possible that your device has been patched against both bugs; Impactor will inform you of this. If you'd like to check before spending time working with Impactor, you can try either the Bluebox Security Scanner or the alternative SRT AppScanner (which I have found to provide fewer false positives than Bluebox's tool).
Some devices are also patched against the second stage now used to get root; devices that are patched will show "link failed file exists". (This second stage was made possible due to help from @giantpune.)
Also, root access isn't sufficient on some devices: in order to write to /system, or in order to use setuid root commands, you might need either kernel patches or bootloader changes.
This tool does NOT work (but is harmless) on: